A 240grain JHP 44 mag will kill a black bear just as quickly dead as anything else given a good hit. No matter what you use you might be engaging this bear in big hurry and up real close. So that's the part you need to consider, the bullets fine for the job. You don't need an exit wound unless you are tracking. I shot a big deer with a 240 grain JHP from a super blackhawk. I hit him in broadside right behind front shoulder but a bit high. The fully expanded bullet was located under the hide at his rump, never took a step. I noticed a big bump on the rump and split the hide and out popped the bullet. I have no fear of using JHP from a 44mag on just about anything. Is there a bullet that will shoot right through the bear, make a 44 size hole and then keep flying? Yes there is. But for self defense that's not always a good thing. IMHO, you have the bullet I would carry.