I have not shot, nor killed, any U. arctos. I am a student of the bullet.
Hunting and defensive-against-toothy/clawed bullets have different requirements. Ditto shot placement.
Defensive bullets need to break enough bone or disrupt enough nerve activity to stop said toothy/clawed critter from injuring you. Straight line bullet travel and deep penetration are helpful for that. Almost any brain hit will suffice. Broken spine helps. Broken neck helps. Blood trail does not help. Bloodshot meat does not help. Holes in bloody organs do not help right away. From everything I have read, you will want instant results. Best to use a non-deforming, or mostly so, bullet. Cast is where I go. No need for crazy hard alloys like lino or stereotype. A heat treated wheel weight will probably be more than hard enough. My air cooled wheel weight 45/70 bullets don't deform much at 15-1800 unless they hit large rocks and they are way softer than buffalo bore's or garrett's bullets.