Bobtails, if it is a copper mine, don't play around. Put the JB on a plastic brush and clean with it this way for 600 rounds, it will smooth out a little bit.
Another product that is similar to JB is the Montana Extreme copper cream, which is what you would imagine JB suspended in oil. The Copper cream is real easy to use on the plastic brushes.
If you would like to speed the process up a little, get some Flitz. Saturate 5 patches with the Flitz, and short stroke the patches in the barrel back and forth. This does lap the barrel a little. Fitz is farily aggressive, so don't overdo this at all. There is another product on the market Called Rem Clean if you can find it. This Rem Clean has 5 micron aluminum oxide in it that will really lap a barrel. I would use this stuf once, and once only. Use the Rem clean on a plastic brush, and when you are done, throw the brush away. Rem Clean is very aggressive.
Montana Extreme Copper killer is the most aggressive copper removing agent that I have every used, and it is an oil based product.
Good luck