Generally, guys will tell you that black bears are easy to kill. I'd say you're putting yourself at risk if this is your mentality. Your 300 WM is a good choice. I've seen black bears fall where they're hit immediately and I've seen big boars take multiple hits and keep running only to fall over 600 yards later with mangled vitals. I've also seen them keep going even when the blood trail ends.
Often times it's not enough to put the bullet in the boiler room on the first shot. Expect to take multiple shots with bullets built to get into the vitals. Any good 200+ grain bullet in your 300 WM will get the job done. Accubonds and Partitions come to mind.