A little surprised no one else had mentioned this, but a 12 gauge for sure, even a 20 gauge slug I'd fully expect to down a 400 pound bear.
Snag a budget/used 870/500 for $200, drop in a slug barrel and have at it. Any of those are minute of bear capable at 50 yards, cheap, capable, proven. Upgrade and personalize it as budget allows and double as home defense.
Multi purpose, cheap, and if you have to, get the 20 gauge for reduced recoil. I bet you know someone who would let you test fire a 12 gauge slug. Recoil won't be so bad if you are wearing winter cloths.