It is kind of counter-intuitive isn't it?
OK here's what I do & it seems to work. I find B/P easier to clean than smokeless & have yet to use or need any bore brushes.
Take a plastic bucket big enough to hold the whole pistol. (this is to stop small parts going down the drain.)
Drop into the empty bucket a cake of regular old soap, the same stuff you wash your hands with. (Personally I use Ivory because it floats & is easy to retrieve).
Fill the bucket with HOT water, as hot as you can stand putting your hand into. (This will dissolve plenty of soap making hot soapy water.)
Remove the wooden grips & set them aside.
Remove the cylinder from the frame.
Remove the nipples from the cylinder.
Throw the whole mess into the bucket of hot soapy water (except the wood grips).
Get your tools while the gun soaks for a few minutes.
Cleaning rod, & loop type tip.
Super cheap hair dryer ($10.00 from wally-world.)
Your preferred preservative, oil grease or whatever.
Take a patch & soap it with the now soft block of soap.
Run the patch through the bore 5~6 times with the pistol mostly submerged still.
Fish out the cylinder & do the same to each chamber.
Find the nipples , stick the toothpick in the hole, & scrub them with the toothbrush.
Use the toothbrush with more soap on it to scrub everything on the pistol. (make sure you get the loading rammer & it's links in both the OPEN & CLOSED positions.)
Lay out 3~4 layers of paper towels, or an old towel.
Fish out everything & sit it on the towels, make sure to count all the nipples.
AFTER checking you have everything dump the hot dirty soapy water.
Refill the bucket with fresh hot water, no soap this time.
Soak swish & dunk everything to remove traces of soap.
Retrieve, count & check as before & fling dirty rinse water. (use fresh, dry towel or paper towels.)
Shake, blow wipe & generally remove as much water as possible from everything.
Put on an insulated glove (clean oven mitt is fine but anything to protect your hand will do.)
Set the hair dryer to "LOW & HOT", or HOT. You need heat for this next bit.
Blow the living daylights out of all the parts. The cylinder, frame & nipples, Remove the toothpicks from the nipples so the hot air gets up inside. Keep going till all the metal is soaked with heat & uncomfortably hot to touch. Remember to cock the hammer & blow down inside the frame, blow up through the trigger guard & into the rear of the frame from the pistol grip.
lubricate everything with your favorite oil, be generous,not shy. Don't forget the bore & chambers.
Grease, not oil is used on the axis pin, the hole in the cylinder for the axis pin & the sliding piston of the rammer. Put a little on the threads of the nipples. (Another toothpick helps as a holder here too.)
Let everything sit till it is cool & reassemble.
You'll hear about how bad petroleum-based lube is for the B/P guns but this only aplies to those areas where there is direct contact with hot powder gas. (bore, chamber & inside of frame). Use of a synthetic oil/grease will solve the problem, or you can use regular old "oil" & remove it with an alcohol wet patch just before firing.