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The largest caliber that you can shoot accurately. If it's a 243, then go with the 243, load some Partition bullets and place one precisely in the lungs-heart area. He will not go more than 50 yards.
I'm no expert (just a hunting newb), but if you are shooting bears over bait, all you need is a 12 gauge with slugs. I took my first black bear with a Foster slug from my smoothbore Winchester 1300 this spring. The holes were huge and the bear dropped and flopped. All I needed was the first shot (although I put two more into him for good measure).
But if you want to buy a rifle . . . well, half the reason to hunt is to justify buying guns .