It is rare for a snake to bite a larger animal. They have to feel threatened before they would risk it. That is why dogs get bit, they attack the snake. If a snake has the opportunity to get away from a bigger animal, they will.
If they did bite a bear, it would depend on a lot of things, size of bear, amount of venom injected, and where the bite occurred. The absolute best place to be bit is on the nose/face. Not much muscle, and no big blood vessels. The venom causes swelling almost immediately, which limits it spread.
So if a snake did bite a bear on the nose/face, it would have a decent chance. If it bit it in a leg muscle, the bear could be killed. Of couse, the bigger the bear, the better its chances would be.
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.