Daryl's last sentence is important. One flannel patch is insufficient to go to the bottoms of the grooves and remove fouling, water, and oil. Turn down your cleaning jag about .020" so you can double your cleaning patches. There should be a significant resistance to pulling and pushing the cleaning rod down your bore. It only takes me about eight strokes to completely flush out the fouling from my rifle barrel. Then I remove the rod from the bore and turn the barrel muzzle down to drain while I dry off my cleaning rod.
When I'm in my shop after a shooting session, I use my machinist's vise with rubber pads to hold the barrel for drying with clean dry cotton flannel patches. The first one comes out with dark grey, even yellow/green oxide. the second often has a bit of grey, and the third comes out almost perfectly white. The forth set of patches goes into the bore easily but is difficult to withdraw as the patches bunch up against themselves in the dry bore. These come out a little shredded or worn looking and perfectly white. Like Daryl, I squirt WD 40 down the bore, wet a patch with the same, and force it down the bore with some authority, to blast the fliuid out the vent. I do this to ensure that there is no water left at the breech face. I have used almost every oil there is over the years, for oiling the bore and outside of the barrel for rust prevention. But now I use synthetic motor oil, and the steel seems to like it. My oiled patch comes out without any additional colour to it, and I find no rust whatsoever in the bore or on the outside surfaces, no matter how long I store the rifle, shotgun, or pistol.
I will also add that at a rendezvous, I almost always clean all the guns I've shot that day in the same water...rifle first, pistol second and shotgun last. My black powder cleaning bucket is a length of black pvc pipe about 15" tall x 4 1/2" in diameter, with a cap glued on. I have a disc of 1/2" plywood in the bottom to support the tang of the rifle barrel. After cleaning three guns, especially the double barrel shotgun, the water is black soup. But I don't bother changing out the water during the cleaning regime.
I remove the barrels from my muzzleloaders every time I clean. I am careful not to slip and mark the stock around the pins or keys, and the pins or keys always are withdrawn and are returned to the stock from the left or off side, same as the lock screws. I confess that the holes around the pins in my rifles become loose after about five years of continually doing this, so I spatula a bit of beeswax over the holes with a small screwdriver, on both sides of the stock to prevent loss of the pins. I find this preferable to leaving the barrel in the wood to clean, splashing fouled water and oil all over the stock, being unsure if I got all the fouling out of the breech area, and having the pins rust in the wood, and become impossible to remove without breaking out pieces of the stock. Just my way of doing this job. I like cleaning my guns and don't find it to be an onerous or tedious job...about 15 - 20 minutes to clean a longrifle. One last thing - I remove and toothbrush the lock in water each time I clean my rifles too. In the shop, the compressor is handy for blowing away the water, and the spritz of WD 40 too, prior to oiling the action and reinstalling the lock.