First, understand WHAT the corrosive element is.
It's a form of salt produced by the primer.
When fired, the primer produces a type of salt, and deposits microscopic crystals of salt everywhere the fumes come in contact.
This was discovered after WWI when the military unpacked rifles that had been cleaned and coated with cosmoline at the end of the war.
They were shocked to discover rifles had rusted UNDER the grease.
A scientist investigated and discovered that the primer in the corrosive ammo was producing a form of salt which attracted moisture and caused rusting.
What you have to do is dissolve the microscopic salt crystals and flush it out.
About the only thing that will dissolve salt is WATER.
There are cleaning materials that contain water and will work, but since nothing is cheaper than water, that's the best thing to use.
To clean the rifle after corrosive ammo, use HOT water to flush every surface the fumes may have contacted.
By using HOT water, the metal will get hot and will self-dry, so it won't rust.
After thoroughly flushing with hot water, clean the rifle as normal with bore solvent, and apply a lube to prevent rust.
Some notes:
Nothing really works as well as water or something that's mostly water.
Many black powder bore solvents are good, but cost more than water.
Some people use Windex, but the only reason it works is because it's mostly water.
Windex CAN be used to "hold" the rifle and do some pre-cleaning by giving the bore and action a good flush at the range.
This will prevent rust until you can get home, if you live in a humid environment, and helps loosen fouling.
NO normal bore solvent or lube will work, unless they contain lots of water.
To test a material for use with corrosive ammo, pour some into a clear glass, and add a little table salt.
Unless the salt dissolves into suspension and "disappears" it's no good for cleaning corrosive ammo.
This means CLP Breakfree and most all other lubes, and most modern bore solvents are useless.
"Shooting the corrosion out" by shooting non-corrosive ammo after corrosive ammo doesn't work.
It "may" blow the microscopic salt crystals out of the bore, but it does nothing for the deposits on everything else.
By using the hottest water possible and allowing the metal to get hot, you prevent rusting since the metal self-drys.
Some of us who take really good care of our guns also clean the rifle AGAIN a day or two later to get any fouling that is in the pores and works it's way out later.
Using hot water to clean the rifle of corrosive fumes is simply a pre-cleaning step that has to be taken.
It's not a substitute for normal cleaning with bore solvent to remove bullet fouling and carbon.