If you're hunting anywhere where the animals can kill you back, I wouldn't fully trust anything less than a .44 mag, especially if you're actually just hunting with the handgun. If it's only serving in sidearm capacity, and you know you won't be running into anything tougher than deer or maybe wolves, a .357 mag is probably a decent bet. It's what I use when black bear hunting, but then again, that's only because I don't have a .44.
If you absolutely must have an automatic, and need to kill bears with it, get a Desert Eagle or a 1911 in .50 AE. You can probably pick a DE up at a pawn shop for around $700-ish. I wouldn't waste time with the ones in .357 mag, unless it also comes with either a .44 mag or .50 barrel/etc.
Then again, if you can't hit shit with a .44, you'd be just as well off with a Glock or something.