I elevate the muzzle, have someone stop the vent, fill the tube with hot water and a touch of soap. I first go in with one of the round toilet bowl brushes attachced to a piece of closet dowel. That is about 3 1/4 inches, and will scoure the rifleing without damaging it. After I have scrubbed the hell out of it, I'll go in with one sponge, the vent still being stopped and force it all the way down to the breech and then pump it in and out a few times, then I'll have the person on the vent step aside and use the sponge as a piston to squirt the water out the vent.
Do it all again, but this time, rather than expelling the water through the vent we depresss the muzzle and use the piston acton of the sponge to help draw the water out the muzzle and drain it. I then prop the breech so the water can drip out. Kind of fun to see that water drip from the top of the muzze from where it has followed the rifling. After it pretty well stops dripping (and while I'm waiting for that to happen I'm cleaning the outside of the tube and the carriage), I go in with a clean dry sponge. Then a washcloth on the worm.
When I'm satisfied it is dry I again elevate the muzzle, pour in a little 30 weight, then with a clean rag on the worm I go in with a lot of twisting action to get the bore oiled. I might then put the rag on the afore mentioned toilet brush to make sure the oil got everywhere. And a nice light coat of oil on all the metal parts, both tube and carriage hardware.