I’ve shot bears with a 10 mm g20, 44 mag lever a 243, 270, 300 wsm, 308, and a bow. Basically whatever I have in my hands at the time will do. They aren’t thick skinned and are pretty soft and squishy in general.
I’ve killed most of my bears with a .30-06 but have killed a few with a 7mm REM. Mag. and quite a few with a .338 Win. Mag. All of these were simply because that’s what I was packing at the time. My wife has killed plenty with her 7mm-08.
I’d have no concerns using a smaller caliber for black bear. I don’t bear hunt anymore to speak of but would have no reservations shooting one with my 6mm Rem.
Shot a nice bear with a 300 WM last year. Planing to hunt with a 7 mm PRC this year. Send a 165-180 grain high quality bullet at 2900-3100 fps down range and all is good.