As a veterinarian, I have treated many snakebites. I have never lost a dog that was bitten on the face, but if bit elsewhere in a muscle, I have lost some of those. Antivenom helps, but due to availablity issues and cost, most people can't afford to use it. An average dog might take 2-4 vials at $300+ each.
From what I've heard, vets are also a little reluctant to use antivenin because the allergic reaction can be worse than the initial problem. Most reasonably sized animals (including humans) are likely to pull through without help, if it isn't a rattlesnake subspecies that has picked up the neurotoxin.
I'd guess a bear is unlikely to die from a snakebite, unless he starves. A bear is also probably less likely to get bitten in the first place...they actually pay attention.