Bears can still think and reason. Zombies, may not be able to for QUITE a while.
Since zombies will have no nerve sensations, they will not be able to tell when their brute strength is injuring them and will soon rip their own arms off, thereby ruining their own efforts.
Bears will be the bigger issue with predator proofing....they can THINK. Plus, I'm pretty sure that animals will be safe from zombies...unless we're dealing with flesh-eating zombies instead of the brain-eating zombies...