I can't comment about the bear, but regarding the Buff, either calibre will do the job, but if you can shoot the 416 comfortably and competantly, then the 416 will do the job better than the 375. Especially on a frontal chest shot, where that big dewlap soaks up an awful lot of energy. I've seen that shot taken numerous times with both calibres and the difference in shot reaction between the two calibres is dramatic.

Have you swept the visioned valley with the green stream streaking though it?
Searched the vastness for a something you have lost?
Have you strung your soul to silence? Then for God's sake go and do it
Hear the challenge, learn the lesson, pay the cost