I had your same dilemma when I started shooting. I shoot Pyrodex in percussion rifled barrels. I read all the reports about just a soapy water rinse would clean a barrel. Never worked for me. The patches would come out clean from the detergent/water wash. First patch with cleaning fluid after the wash came out dirty, even when I didn't use a brush. Tried hot water, cold water, different cleaning solutions, longer pumping sessions, same results. It also didn't get the residue around the percussion cap clean.
The "pumping in the bucket" method may get a smooth bore acceptably clean. When you try it in a rifled barrel, its still dirty. Its not copper residue from the brush turning your patches dirty, its spent powder. The soapy water does not get the spent powder out of the rifling.
"Pumping" is a good start but your patch soaked in cleaning fluid will always come out dirty afterward. Just run 5-6 with cleaning fluid thru the barrel until they come out clean. I use patches soaked with Barricade.
I'm sure many on here will dispute this but I challenge them to run a cleaning fluid patch thru after their water wash. They get to a clean dry patch stage and consider it done. Even had a guy on here try to tell me the Barricade was reacting with the metal to give me the black color!?! Then there's the camp that will tell you that its "flash corrosion" that's giving you the black color. Trust me, corrosion doesn't happen that fast and it's not black in a steel barrel. Then there's the purist camp that will say it's the Pyrodex and I should be shooting real black powder and all my troubles will go away. Well I tried that also with the same results.
I think most people just want to shortcut the tedious cleaning of a black powder weapon.