Clean with solovent on a brush, then some patches. If it is not heavy then that should do it. If it is heavy wrap a strand or two of a copper (test it with a magnet first) around a bore brush. Some solvnet, then a few clean patches.
Note for my .41 mag RBH I use M-pro7. I spray a bit on a patch run it through the bore a couple of passes, then do the same with the cylinder chambers. Let it sit for a couple of minutes. Spray a touch on a brush, run through a few passes in the barrel, then cylinder chambers. Follow with a wet clean patch. I then pass a dry patch through the barrel. Oil, then another dry patch. Takes me less than 10 minutes at the range while the gun is still warm.