You have gotten a lot of great advice from some very experienced black powder shooters. I don't know if I will add much to what has already been said but I will toss in my cleaning procedure for your amazement, amusement and edification. Here is how I do it.
Since you have found some rust in your bore, but not enough to be a major concern, I would recommend that if you are still getting rust out of your bore, that you use one of the 3-M green scouring pads to scour it. They are the kind that you use to scour pots and pans. You will need a jag that is smaller than the one that you normally use for your cleaning patches. The scouring pads are thicker and need a bit more clearance. Put some oil on the piece of 3-M scouring pad and use it to scrub the rest of the rust out of your bore. Then wipe out your bore with several cleaning patches. Once it is clean and your patches are coming out clean, use some good gun oil such as Birchwood-Casey's Barricade to oil and protect your bore.
To clean your gun after shooting it, you will need to remove the nipple and put it in a small container of warm soapy water to soak while you clean your rifle. They make a device, a piece of tubing with a nipple attachment on it, to attach to your rifle by screwing it into the nipple hole. It is worth the money and you will find it a great help in cleaning your gun. Screw it into the nipple hole and put the other end into a can of warm soapy water. Put a wet patch on your jag and run it down the bore of your rifle. You will see bubbles coming out of the tubing. Make sure that you have the tubing where it won't come flying out of the can when you pump the water into your bore. If it flies out, it can be pretty messy squirting dirty water all over the place. Anyway, pump soapy water in and out of your bore until it looks clean. Then rinse your bore with clean water to remove the dirty soapy water. Dry with several dry patches. The next step is an important one and that is to spray some WD-40 down your bore (hold it vertically so it will drain out the nipple hole) to remove the last traces of water. That is the main purpose for the invention of WD-40, to disperse water. Now, run several patches through the bore to remove all of the WD-40 (it is not a rust preventer in spite of all claims to the contrary). Follow this with a patch with a good gun oil such as Barricade to oil and protect your bore and you are good to go. Of course, you should have cleaned the hammer face and around the nipple with a tooth brush and soapy water to get those areas clean and you need to use the toothbrush on the nipple that you have been soaking. Brush it and rinse it and spray it with WD-40. Put a tiny bit of grease on the threads. Be careful not to get grease in the hole in the nipple, just on the threads. This will make the nipple easy to remove the next time you are ready to clean your rifle. I like to put a light coat of wax on my stock to keep it looking nice. My favorite wax is Renaissance Wax. It's pricy but a small jar will last you for years....maybe decades. If you don't want to spend the money for the excellent Renaissance Wax, Johnson's paste floor wax will work, too.
Oh, I almost forgot, you need to give some attention to your lock as well. Just remove it by removing the lock bolt. Unscrew it until it is almost all the way out and then give it a few taps with something like a plastic hammer or a piece of wood to knock the lock out of the mortise. When it is out of the mortise, finish unscrewing the lock bolt. Put it aside in a safe spot where it won't get lost. Now here is another of my cleaning "secrets", go to your local auto parts store and get a spray can of either brake cleaner or carburetor cleaner (both work equally as well). Take your lock outside and spray it with the spray cleaner to flush out all of the crud. Shake off the cleaner and let it dry. It will dry very quickly. Then lightly (just a tiny drop) oil the working parts and wipe the whole lock with a very light coat of oil. Do not use grease or oil the lock heavily. It won't make the lock work any better and will just gather dirt and crud. Replace your lock and when you tighten the lock bolt, do so gently. All you want is for the lock bolt to be just snug. Over tightening can cause problems. Gently snug and then stop.
Anyway, that's my cleaning procedure. Others may differ but that is what has worked for me for quite a few years and I have no rust problems. My rifles all look like new....except for a few wear marks and the occasional minor ding. :hatsoff: :hatsoff: