Black Bears
I've shot upwards of 30 (government job-camp protection) mostly with a Model 94 (.32 Spl) and a few with a .303 British.
Males ran avg. of 250 live weight, females maybe 150 or so.
Some were DRT, but I've also seen them run (away from me) for 100 yards, full bore, then drop.
If your bears are similar size, you're fine, but I'd suggest those 165 gr. bullets.
But they can be surprisingly tough some times.
One trick: they have superb noses, but poor eyesight. If I caught one with its head down or behind brush, I'd put the sights a couple of feet over the middle of its back, then whistle. Bear stands up for a better look and is right in my sight picture.