Be careful with rust. Rust is steel/iron cancer. Even a little is bad. It frosts the surface, making it more prone for a repeat attack. Like cancer, it has to be cut out. If you find a tiny film of rust on a dry patch several days/weeks/ after cleaning, scour the bore with OOOO steel wool on a tight jag, or a smaller jag and a square of scotch brite. Keep your bore completely free of rust.
When my late friend Peter Nicholson got started in muzzleloaders, I told him to clean with hot water out of the tap, because that's how I did it at that time. He interpreted that to mean the hotter the better, so he used water just off the boil. He flash rusted his bore every time he cleaned it. He sure got the fouling out, but he introduced iron cancer, and it got worse and worse until he nearly ruined that Getz .40 cal barrel before he told me about it. Daryl and I spent several days lapping the bore, and we eventually got it smooth enough that it can be shot all day without cleaning, but it was almost lost.
I now use only cold water, and now I do not get any brown on my patches. My rifle bores are a lot happier.