I used to have an old bench rest buddy who, with regard to barrel break-in would say, "do it however you want, chances are, you'll be wrong anyway". With centerfire, I would clean after each of the first few shots, maybe 10, then go to every 2 or 3, keeping that up for 25 or 30 shots. I didn't want to shoot a lot of rounds, since those barrels didn't usually last but a season anyway. With air rifles, I just clean a new barrel and start shooting normally. Most of them need cleaning after a relatively few shots at first, then get more seasoned with longer intervals. I don't polish or use a bronze brush unless the barrel needs it. Some folks say a bore scope would indicate they all need it. May be, but if it's shooting to my satisfaction, I don't much care what a scope might indicate. I'm an old retired fart and I like to shoot, not clean, so I shoot, usually works out okay. During the last couple of years I've had two barrels that wouldn't shoot, and both were replaced under warranty. I gave each a single polishing session, but I don't think any amount of polishing would have brought either around, figured I paid enough to have a barrel that shoots, and the seller didn't disagree.
Just trying to make sure you get the correct information for the question you are asking.
