First off, what kind of powder are you using? 777 and BlackMag are easy since they clean up easily with patches soaked in warm water. Just use 5-7 soaked patches, by then they should be coming out pretty clean. Then use a couple dry ones. Then let the barrel sit for 10 minutes to evaporate remaining moisture and lightly oil with a last patch.
Pyrodex is more difficult. I still use the patch-only method, no soaking. It just takes 2-3X as many patches. I use Q-tips to get the nooks and crannies, the bolt and breech area, etc.
While it won't allow you to use a bucket of water, quick-release rings (I got mine from Leupold) allow easy scope removeal for cleaning and returns the scope to the point-of-aim when it goes back on.