The 8mm-06 with a 200 grain partition!

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.

Myself personally would use either my 270win wint 150gr bullets or my 7.62X 54mm with my yellow tipped high ocktaine military surplus bullets, if these or my 44mag ruger don't work I could always borrow my brother's late father's (Vietnam sniper/gun smith) custom 7mm rem mag built on a sako action, a custom stock and a lathed barrel.