Some other thoughts
If I were hunting bear at shorter ranges (< 125 yds.) over bait, I'd probably go for a semi-automatic (like a BAR) or a lever action. Something with ability for a quicker follow-up shot, in case you tick him off and he decides to attack.
I'd go with a Marlin lever action in 44 Magnum. Plenty of juice to take down even the biggest black bear. I'd carry my Ruger Redhawk chambered in the same round as a back-up.
Failing that, a Marlin lever action in 30-30.
There's no reason to punish your shoulder or your wallet with a hotter round.
If you want to be able to use it later for longer shots on elk, I'd goo for either a Savage or Ruger bolt action in 308 Win. (308 Win can be a bit more accurate, as stated above, and this, to me, is more important than ability to carry a slightly heavier bullet, because shot placement is more important)
I'd be nervous with a bolt action for close-range bear though.
Go with the lever action in 44 Mag or 30-30 and you can justify another rifle purchase later if you decide to go after elk at longer ranges. (44 Mag is probably 125 yd cartridge, while 30-30 is probably more like 200) Peep sight, iron sight, or 2.5X scope would be good for the closer range lever.)