This is a very complex question. It gets into the subject of "just what does the 14th Amendment cover, and how?"
OK. History lesson time.
The Constitution we live under now was passed before the Bill Of Rights. BUT inclusion of a BoR was part of the deal leading up to the Constitution so they are definitely integrated.
The Constitution is binding on the states:
Article VI
All debts contracted and engagements entered into, before the adoption of this Constitution, shall be as valid against the United States under this Constitution, as under the Confederation.
This Constitution, and the laws of the United States which shall be made in pursuance thereof; and all treaties made, or which shall be made, under the authority of the United States, shall be the supreme law of the land; and the judges in every state shall be bound thereby, anything in the Constitution or laws of any State to the contrary notwithstanding.
Once an Amendment passes, it has the full force of the Constitution:
Article V: The Congress, whenever two thirds of both houses shall deem it necessary, shall propose amendments to this Constitution, or, on the application of the legislatures of two thirds of the several states, shall call a convention for proposing amendments, which, in either case, shall be valid to all intents and purposes, as part of this Constitution, when ratified by the legislatures of three fourths of the several states, or by conventions in three fourths thereof, as the one or the other mode of ratification may be proposed by the Congress...
The Bill Of Rights has a Preamble that practically nobody takes notice of outlining it's purpose:
THE Conventions of a number of the States having at the time of their adopting the Constitution, expressed a desire, in order to prevent misconstruction or abuse of its powers, that further declaratory and restrictive clauses should be added: And as extending the ground of public confidence in the Government, will best insure the beneficent ends of its institution.
Source:
http://billofrights.org/
If it's not clear yet, the stated purpose of the WHOLE BoR (proposed as a block!) is to limit abuses of powers - not to ensure specific government powers.
Based on the above, you can make a damned good case that the original intent was to limit ALL government powers, including the state.
In 1833 the US Supreme Court put a quash on that concept in Barron v. Baltimore:
http://laws.findlaw.com/us/32/243.html
Mr. Barron's boat docks were hosed by the town of Baltimore. Barron sued for improper "takings" without due process, and lost. The US Supremes decided that the BoR didn't apply to state (or local) governments or their actions.
It is impossible to overstate the level of civil rights violations this triggered. "Bad decision" doesn't even begin to cover it.
By 1858 the state of South Carolina declared the death penalty for any preacher supporting abolition (anti slavery) from the pulpit. Suppression of the written word was common as the South slowly turned into one giant Gulag. (And yeah, I know this paragraph will honk some people off around here but get over it, I can back that statement in spades.)
In 1856 the US Supreme Court issued one of their most infamous decisions ever: - Dred Scott:
http://laws.findlaw.com/us/60/393.html
The court came to a decision that was morally horrendous but legally correct at the time: that America had always been a racist nation, that various founders of the US were racists who supported racist laws, that racist laws existed at the time of the founding, before that and after. They cited genuinely nasty examples from the 1780s and thereabouts.
They therefore didn't just support slavery, but racist laws. In doing so, they said that blacks didn't have the "privileges and immunities of US citizenship"
and they exhaustively defined the term in this key quote:
For if they were so received, and entitled to the privileges and immunities of citizens, it would exempt them [blacks] from the operation of the special laws and from the police regulations which they considered to be necessary for their own safety. It would give to persons of the negro race, who were recognized as citizens in any one State of the Union, the right to enter every other State whenever they pleased, singly or in companies, without pass or passport, and without obstruction, to sojourn there as long as they pleased, to go where they pleased at every hour of the day or night without molestation, unless they committed some violation of law for which a white man would be punished; and it would give them the full liberty of speech in public and in private upon all subjects upon which its own citizens might speak; to hold public meetings upon political affairs, and to keep and carry arms wherever they went. [emphasis added]
Note that the "privileges and immunities" clearly includes the 2nd Amendment, but also some surprises: "the right to travel without pass or passport"? What they're doing is describing "the traditional rights of free Englishmen", which can be translated as "the BoR and then some".
The BoR does not define our whole set of rights.
1861, the Civil War starts, ends 1865. By which time slavery has ended BUT Dred Scott's support of racist laws is still in effect. The South rapidly passes "black codes" such as:
1. That it shall not be lawful for any freedman, mulatto, or free person of color in this State, to own fire-arms, or carry about his person a pistol or other deadly weapon.
2. That after the 20th day of January, 1866, any person thus offending may be arrested upon the warrant of any acting justice of the peace, and upon conviction fined any sum not exceeding $100 or imprisoned in the county jail, or put to labor on the public works of any county, incorporated town, city, or village, for any term not exceeding three months.
3. That if any gun, pistol or other deadly weapon be found in the possession of any freedman, mulatto or free person of color, the same may by any justice of the peace, sheriff, or constable be taken from such freedman, mulatto, or free person of color; and if such person is proved to be the owner thereof, the same shall, upon an order of any justice of the peace, be sold, and the proceeds thereof paid over to such freedman, mulatto, or person of color owning the same. [Ed. note: the off-duty fashion choices of “justices of the peace, sheriffs, or constables” at that time tended toward an ensemble of basic white bedsheets with eyeholes...especially at night.]
4. That it shall not be lawful for any person to sell, give, or lend fire-arms or ammunition of any description whatever, to any freedman, free negro or mulatto; and any person so violating the provisions of this act shall be guilty of a misdemeanor, and upon conviction thereof, shall be fined in the sum of not less than fifty nor more than one hundred dollars, at the discretion of the jury trying the case.
Alabama statute of 1865, from “The Second Amendment: Towards An African-Americanist Reconsideration”, footnote 178 — two more state-level examples precede that one.
http://www.guncite.com/journals/cd-recon.html
The Federal gov't decided to put an end to this sort of thing, led by abolitionist Ohio Republican John Bingham, primary author of the 14th Amendment of 1868.
To do so, he decided to turn the words of Dred Scott back on itself. Note the opening paragraph of the 14th when read through the "prism" of Dred Scott:
Section 1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
Got that? Blacks become citizens, and then "No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States".
It gets better. At this moment in 1868, blacks did NOT yet have the right to vote. They didn't have "political rights", only "civil rights". Yet Bingham and company were openly saying that the 14th was meant, in part, to arm the new freemen against Klan attacks.
So the right to arms was transformed from a political right tied mostly to "militia duty/right" which in turn is akin to the right and duty of jury service - something else blacks didn't get until the 15th Amendment of...1872 I think?
And the kicker? In 1868 we're no longer talking about muzzle-loading flintlocks. The Gatling Gun was in production, as were 15-shot Henrys and a slew of revolvers...including metallic cartridge designs. The Mormons had invented the big-bore snubby for God's sake (pardon the pun).
So what did the Supremes do? In a slew of cases they pretended to have no clue what the hell "privileges and immunities" were. TO THIS DAY they have maintained this fiction. Prominent justices throughout the 20th Century argued otherwise to no avail. If you want to see how bad it got:
http://laws.findlaw.com/us/92/542.html
http://en.wikipedia.org/wiki/Plessy
http://laws.findlaw.com/us/170/213.html
The first of those (Cruikshank) was in my opinion the worst. It said that despite obvious evidence of civil rights violations, the US Federal Gov't could not punish a set of actions by state and local gov't actors. That was left "up to the states". The defendants in Cruikshank responded to blacks attempting to vote by first disarming them (2nd Amendment violation), launching days of rape, riot, arson and murder (violations of right to vote under the 15th Amendment, right to peaceful assembly under the 1st, etc.)
All defendants were turned loose and the first American civil rights movement died in it's tracks.
This next bit is speculation on my part: I believe that in 1909 the US Supreme Court got their noses rubbed hard in just how much horror they had allowed:
http://www.law.umkc.edu/faculty/projects/ftrials/shipp/trialaccount.html
I *think* the Shipp case was instrumental in the next steps.
In a series of cases throughout the 20th Century, the US Supreme Court decided that certain civil rights, as they came before the court, were "fundamental" and therefore denying them would be a violation of "due process".
What they invented was "selective incorporation" of the BoR against the states, one civil right at a time, starting with pieces of the 1st Amendment and working their way through the BoR.
As of this writing, all elements of the BoR except three have been incorporated ("enforced") against the states:
1) The 3rd Amendment (quartering of troops in people's homes isn't popular anyways...)
2) The 5th Amendment right to indictment for major crimes by grand jury. Which has in some states (esp. California) weakened the grand jury system, which is a problem...
3) You guessed it: the 2nd Amendment.
The whole concept of "selective incorporation" through the due process clause was a steaming pile the moment it was thunk up. It was a "kluge", a way of making social change in a "controlled fashion". But it was and remains a fraud, designed originally to give minorities limited civil rights instead of "all in one shot". It was wrong from day one and remains so: civil rights don't work based on what "the powers that be" are comfortable granting.
In a fairly recent decision supporting the idea that states don't have to honor the 2nd Amendment, California Attorney General Bill Lockyer-D cited US Supreme Court precident for such a position.
US v. Cruikshank.