When I first started muzzleloading I was told by one of the older blokes that modern detergents, fairy liquid and the like, contain pure salt to make them froth up. He said use Stardrops there is no salt in it. I have been using it ever since and found it works.
When I clean my bore I use a wool mop and stand the barrel in a bucket of hot water and use the mop like a plunger, going up and down and drawing the water through the barrel until it comes out of the muzzle. I change the water for a second clean and then I change it a third time but without soap so I can flush everything out and then I dry the barrel with ordinary patches. Then I oil it. I have never had any problems with rust using that method.
Everyone has their own method and they all work. It is essential the barrel is dry before oiling it. Don't bother with WD40. It will remove moisture but it does NOT stop rust forming.
Before I put the gun away I put a small piece of cloth on the nipple and lower the hammer to hold it in place. I find this stops any excess oil draining out and going on the woodwork and the cabinet floor.
I usually run a dry patch through the gun before I go out with it so it is free of oil so when I flash off and any excess is burnt off or blown out of the nipple to reduce the chance of a misfire.