175 Nosler Partitions through the lungs and you'll have your bear. Just accept the fact that your guide will be in full readiness to back him up if the 7 doesn't flatten his bear!
I'm not arguing about a bullet thru the lungs killing the bear.
I wouldn't be shooting at the lungs in all situations. I would want a bullet I could count on to ANCHOR the bear.
I would choose one of the 175s already listed by SKane.
That from my ZERO experience in bear hunting! I believe in being prepared for the worst case scenario !!