I shoot 175gr Matchkings 1/4 moa out of my 1-12" 308.
That said, as far as hunting bullets go, you should be able to sling most all of the regular 180gr offerings just fine.
Heavy bullets are not needed for black bear, anyway. I would run 165-168s and not sweat it a bit. Lighter bullets than that would work, but that is just what I prefer....