I have two guns listed on my ATC, my primary is a .44 and my back up is a .357. Here's the deal on shooting a bear in the chest in a defensive scenario, put 5 in the bear and save one for yourself. A chest shot is a killing shot, but its not a stopping shot, not with a .357 and not with a .458. In a defensive shooting scenario, the bear by definition is close to you, adrenalined up, and you need to stop his forward progression. Typically black bear attacks are predatory in nature, so playing dead if you haven't stopped him could result in unpleasant consequences. The point of shooting is to prevent him from making contact, if he can't touch you, he can't hurt you. The only shot from a handgun that works is a brain or a spine shot. I'd avoid the big bone breaking shots that I might try with a rifle or a shotgun, except in dire circumstances; like the bear was already on top of another person; then you'd want to break his hip, A) because this keeps the bullet away from the mauling victim, B) because it will distract the bear from causing further injury to the victim, and C) gives you the time and position to make a killing shot without endangering others. But even at close range the spine and brain present small targets, and if you don't practice regularly, and pre-program yourself as to how to find your target and shoot quickly, the odds are against you.
I think your choice of a 686 with a 4" barrel is fine, wear it in a holster that will allow you to move around aggressively without loosing the gun, but allows you to draw quickly. Practice your draw by the numbers until you have your draw and firing stroke perfected. Practice at ranges from contact close out to about 10 yards. Don't shoot too soon. Shoot DA only. Forget anything you've ever heard about shooting center of mass. Concentrate on being able to place your rounds in a group 2" wide by 3" high. If you can, you're shooting too slowly, if you can't you need more practice. If the bear is facing you, his brain is only the width of his snout, and is located behind his eyes and ahead of his ears. The massive width of his head can make finding the brain confusing, and the motion of his head won't help. But if he's about to attack, his focus should be locked onto you, and his head should be more or less stationary, any lateral movement will only mirror his body movement as he approaches.
Don't choose the hollow point loads that are normally sold for self defense. Penetration trumps a wide wound channel; instead search out a heavy for caliber hard cast WFN or a SWC, bullets or a truncated cone jacketed bullet. Seeing that you'll be in the States, my top choice would be Corbon's .357/200 gr WFN, listed by them as 357 Mag 200gr CORBON Hunter HC. With that load I'd carry a .357 for bear work without hesitation. My .357 load is a 195 gr SWC over a stiff charge of H-110 that trips the chronograph at 1150 fps from my 6" M-27. Corbon's 200 gr WFN at 1100 from a 4" revolver would be better; Corbon claims 1150 from a 6" barrel. If you roll your own, WFNs heavier than 180 grs can be had from a variety of makers, but if you are down there for a short period of time purchasing a few boxes or factory Corbons might be more convenient, if a little expensive.