When I do a bore with JB Bore Paste..
Start on a very clean bore. Then with a quality gun oil, oil the bore of the rifle. Now is when you take the bore paste and apply it to a cotton patch. This must be tight fitting. Apply a good dab of the paste, and kind of smear it around that patch. Then push down without stopping, and pull back up with out stopping. That is one stroke.
I do 20 strokes then change to a new patch and more paste. Usually 100 strokes is plenty to smooth things out and really clean the rifle. That bore after you clean out the bore paste will really shine.
I have never had JB Bore paste hurt any of my barrels. It removes fouling, crud, copper, lead, plastic, and all the other nasty things out of the bore. I do my rifles I shoot a lot about every six months. But on their follow up cleaning only give them 40 strokes.