What you've got will work fine on black bears. Use a tough bullet so it can break bone and still deliver a killing blow down deep. Most bears you meet in the woods won't be any bigger than the deer but every now and then a big bruin will show up that will scare the heck out of you. Trust me there is a world of difference between a 150 pound bear and and a 350+ pound beast. It's when you meet one of the big ones that you really want the extra lead to counter big pile of mussle, tooth and claw coming your way.