I'd say that you would need to use toughest bullet you can - you need to be able to punch through heavy hide, bone, & meat. This would eliminate any of the ballistic tipped bullets. I would suggest using something like a Nosler Partition or the Combined Techolgies FailSafe. Any of the non aero-tipped bonded bullets on the market now would also get the job done well I believe.
These would be my choices for bear if using a centerfie rifle. Personally I'm saving my LARGE game hunting for my muzzleloader............ I'm getting brave in my old age!