I talked to a relative who has shot lots of bears. He says a .243 is plenty if you are in a tree and shooting for the spine.
Where you hunt bears may be different than Minnesota but the brush is so thick that finding them after you kill them is the challenging part unless they leave a good blood trail you may never locate them.
I don't think they are that tough to kill just tough to find afterwards. Especially if they can crawl under a log or get into the swamp.
whelennut

I like to do my hunting BEFORE I pull the trigger!
There is only one kind of dead, but there are many different kinds of wounded.