Yogi can run at 35 MPH flat out. That's under 6 seconds to cover 100 yards. A powerful handgun, that a .357 is marginal as such with any bullet, requires you to be able to recognise the threat, draw and fire, accurately, in that time.
If Yogi is in camp, you won't have time. In any case, a shot will need to be put into his central nervous system. That's his head or neck. Both decidedly small targets when the pucker factor is high. Breaking leg bones, that a .357 isn't likely to do on anything but a blackie, won't necessarily help either.
Anyway, most American hunters carry a hand gun because they can. Not due to any real need. Yogi really isn't interested in you. He might be interested in the gut pile left after dressing a deer, but you are nothing but trouble as far as he's concerned. Yogi and Cindy will defend themselves(or the cubs) if you come across 'em from up wind, but they aren't out looking for you.