The heavy bullet advice that others are giving you is GOOD advice.
Black Bear are easily killed with any good deer gun as long as you get good penetration. Too much velocity causes bullets to 'blow-up' and impedes penetration.
If you handload I'd suggest you use a 160 grain Nosler Partition or any weight of Barnes X bullet from 130-150 grains. They will shoot right through an average black bear and give great wound channels too.
I have a 270 WSM and have only killed a few animals with it, but it chronographs only 100 FPS faster than my 270 Winchester (which has a 25 inch barrel) and I have killed more game than I can count with my other 270s so I know you'll have good luck with those bullets.
Think of the magnum as a standard 270 with an extra 65 yards of range.
The velocity of the WSM at 65 yds is the same as the 270 Win at the muzzle.