Dan's method will work very well if the barrel is left on the gun. It just takes a LOT of patches.
We (Taylor and I along with everyone who owns one of his rifles(that I know of)) remove the barrel for cleaning. With the longrifles, I leave the rod in the pipes as added strength
to the wimpy stocks & gently set aside the stock. The locks and barrel are both removed and the barrel is submerged into a container of water, usually a 1 gallon stainless pail.
I clean my guns more like SmyleeG. 6 patches and it's done. Sometimes, depending on temperature, 4. It take me one to clean, and 4 or 5 to dry and oil.
The important thing is tepid water - cool or cold. Hot water can cause accumulative rusting/pitting problems. We've had to lap more than one pitted barrel due to the person cleaning
with HOT water.
Some folks have noted the dark grey streaks on patches after the bore has been dried, as-have I. For me, these turn red with rust over night, so they are caused by picking tiny bits of
metal (visible, not microscopic) off the barrel due to friction of the cloth, I assume. I've been told these dark streaks are "carbon" fouling from the powder, however I ran some carbon solvent
down the bore and that came out without ANY discoloration. Must have been from the steel itself.
As well, after the bore is dry & the last drying patch is almost impossible to pull out of the bore, the WD40 spray, then patching, that patch comes out wet with WD40- no streaks either. Same
thing days later - wet is all.
The whole cleaning process takes 5 or 6 minutes is all. It takes much longer to "properly" clean a modern rifle barrel.