old fart: it isn't the caliber, it is the load. The last I used soft nosed 357 slugs on a black bear sow (late 60s) and they were the wrong loads; they would not penetrate the grizzle plate or her tough skull worth a darn - just like Milek's soft nosed loads. She put me up a tree and the last shot was to her left eye socket at about 3 feet distance and that killed her. That is when I learned about hard cast semi-wadcutter slugs and have used them since.
My preferred cast loads at the time used the old Keith (Lyman) 358429 that weighed about 170 gn and in encounters with other black bear out to 25 yds those slugs, over a max charge of 2400, would penetrate t&t the chest or bust the on-side shoulder and pass through the chest. I always add a 'finisher' and never had any of those hard cast Keith slugs slip off a skull.
Bear have rather sloped foreheads, or at least the ones I have dealt with have had fairly drastically shapped (sloped) foreheads and soft nosed slugs have a tendency to deform, flatten and/or skid off the sloped part of their skull. If your hard cast square shouldered or flat nosed slug hits square on it will penetrate. A parallel can be taken from a Elmer Keith encounter with a bull and a 38-40. Keith liked the 38-40 cailber, experimented with it and handloaded for it. He was carrying his 38-40 one day when he 'had a encounter' with a angry bull and had to dispatch it. He fired his first shot, a factory 180 gn 3/4 jacketed soft nose dead on into the bull's skull and the bullet flattened and popped off, just angering the bull more, which almost got Keith and his horse killed. Keith lambasted those factory slugs as near useless but almost forgot to mention that the second shot fired, one of his 38-40 handloads with a hard cast slug, drilled the bull straight through the skull, dropping it immediately.
I would not feel undergunned or under-armed with a 357 in Black Bear country. My 357 is a 3.5" Model 27. I now make up for the short barrel by using heavier bullets and have preferred the 200 gn hard cast more traditional style semi wadcutter from either Colorado Cast Bullets or Mt. Baldy Bullets. Ron Reed (Reed's Custom Ammo), one of our Moderators makes another style of 200 gn, gas checked, semi wadcutter that wears a larger metplat than the same weight Keith style slug and is a wicked lookin' long heavy bullet. I load my 200 grain slugs over a old Winchester factory load of 296 powder that gives me lower pressures with the 200 gn slugs than with the 158 grain slugs. If you handload at all I feel the 200 gn slug would be the load to use in your 357. jmtcw. Mikey.