I've lost track of how many bear kills I've been a part of, maybe 20? Smallest caliber was a 6.5 Grendal. Also used 308, 358 Win, 30-06, and 375 Ruger. Basically any deer cartridge will work. I'm sure a .223 would do just fine (it's been done). But a bloody exit is nice for tracking. I'm not saying it will kill the bear faster, just that if the bear runs into the brush an exit is nice. On black bears (up to a respectable but not obese 6 footer) a 6.5 Grendal mafe exits and left good blood trails except when it hit a shoulder. It demolished shoulders but didn't exit. The .308 exited every bear except a grizzly with an angling away shot (not a shot I'd take on an unwounded bear). Bigger caliber exited with all readable shot placement on black bears.
So to conclude. I don't see any reason to go above 6.5 Creedmore/308 for black bears. The 358, 30-06 and .375 didn't kill faster. You can go smaller if you want and many would argue for a 6mm ARC or .223 on the theory that you'll shoot it better, practice more, etc. I see that as more of a long range argument. In close brush I'm confident I can shoot any reasonable caliber well enough that it won't matter. In that scenario I like a guaranteed blood trail. So the 6.5 Grendal to 308 class calibers would be my choice.
More important than caliber is knowing bear anatomy and putting it in the vitals (bears are not deer).