Sharp shooter - I use BB in every one of my 6 or so sidelocks and I've never had a rusting issue. And one of these rifles I've owned since the early 70s. After a shooting session, I always swabbed the bore out before I left the range with T/C #13. No I use T-17 as Sabotloader mentioned.
When I get home, I strip the rifle(s) down and give them a hot soap and water bath - first with a nylon brush then patches. Then a hot clean water rinse.
The trick with using BB is to be sure the barrel is completely dry and hot before application. Before I apply it after the rinse, I dry with patches, then an alcohol moistened patch and another dry patch. Wait a min or two and apply the BB sparingly.
A lot of shooters do not use it and would rather use a quality gun oil. And that's fine. I just figured if it ain't broke, don't fix it. And BB works for me.