On your person, you can carry in the open, but not concealed. Some cities/counties/towns have old laws regarding open carry and you will be arrested if you have no CCW permit.
For carrying in a car, VA law is vague and it will depend on where you are, and if you inform the officer you have a gun, he will likely tell you just to keep your hands in plain sight. He may separate you from the weapon while he runs wants & warrants or he may ask you to stand where he can watch you or the other occupants of the car. Some officers will consider a weapon concealed if they can't see it, but others won't care if you let them know about it right away.
CCW depends on whether you have a permit issued in VA or a reciprocating state.
BTW, how will the officer know unless you tell him? He can't search your car unless you let him or he has PC. If he asks, he doesn't have PC and you can say "No." All of which is avoidable by having a CCW permit.
People get arrested daily for doing nothing more illegal than offending a cop.
I'm afraid it takes a little more than that unless you are stupid. In most cases an officer will need to obtain a warrant before he can arrest, and is seldom able to detain you while a warrant is obtained. With the prevailance of video cameras, you don't find too much that people are arrested for that isn't legit. If you have bad experiences with a cop, document it, and try to get evidence. It will be obvious to all parties that the cop is harrassing, and he will likely lose his job. Generally, unless you give him a reason, cops will never even talk to you unless they know you or want your phone number.
As many cops are against carrying,
Not true. In places such as LA, NYC, Chicago, DC, and others with strict gun control, the guns LEOs encounter are usually possessed by criminals. You can't blame them for looking closely at you if you have one on the front seat. It's true that most Chiefs of Police are against the public being armed, but most street cops are pro-RKBA.
they arrest you for causing a disturbance or some such nonsense. Easier said than done.