more important than caliber, bullet choice is a bigger factor.
the 06 is my minimum choice...
you will do fine with it.
and you are looking at the right bullets!
federals bear claw ammo is great for black bear.
as is remington a frame, and barnes bullets.
the nosler partition is also a good choice, and would be the "softest" i would think of using.
bye a box of each, see what one your rifle prefers, and go with it!