Now push a couple of dry patches down the barrel with a jag to remove the dirty solvent & loose fouling. Next spray some foaming bore cleaner in the bore and set the barrel aside. If the gun is a revolver you can set the whole gun aside for awhile until the bore cleaner does its work (read the directions on the bore cleaner you’re using). If you have a semi-automatic then you can clean the other parts while you leave the bore cleaner working.
After waiting an appropriate interval (per the bore cleaner instructions), run a clean, dry patch through the barrel using a jag to push out the solvent/cleaner & dissolved fouling. Put some nitro solvent on a bore brush (or spray it into the bore), run the brush through the barrel a few times and then follow with a dry patch. Spray the bore full of foaming bore cleaner and leave it until the next commercial break on TV (10 or 15 minutes ) and then repeat the “nitro solvent/brush/patch/bore cleaner/patch” steps until the dry patch after the foaming bore cleaner comes out clean, not brown/black, blue or green. Now the bore is clean.