The question might be how quick do you need it to be? BP because of it's nature is going to take more time than smokeless. There is more fouling and that fouling causes rust.
Unlike a modern firearm where you can give them a quick pass through, a wipe down, and a coating of spray, or dunk the entire handgun in a bucket of solvent, remove and let it drain.
Water, a brush, some patches, followed by a rust inhibitor will work fine.
Some folks like warm water, some add dishwashing soap. Now if you use
petroleum based lubes, or a grease made from something like a food grade oil or fat, you very much may want some dish soap, perhaps even Dawn brand, the same stuff they use to get the petroleum based stuff off of animals in an ocean oil spill.
Some folks have reported they used generic windshield wash fluid intended for use in a car, or Windex to also clean barrels,
followed by a clean water rinse.
Some folks use a mixture of equal parts of Murphy's Oil Soap, hydrogen peroxide, and rubbing alcohol, again
followed by a clean water rinse.
If you are shooting a cap-n-ball revolver, using grease on the chamber mouths to prevent a cook-off, remember too that you are going to need to remove the nipples when cleaning in most cases. (actually any gun using a nipple with a cap, or even most inline using a primer should have that portion thoroughly cleaned.) You will need to clean the threaded portion where the nipples are held with cotton swabs and again apply rust inhibitor before replacing the nipples. Revolver cylinders can be tedious to clean..., but I have never been able to avoid rust around the nipples unless they were removed and the threaded sockets also cleaned. Others may have had more success.
Just remember that final good coating of rust inhibitor when you are done, and check the gun 24 hours later for rust to be sure you didn't miss a spot or two.
LD