How do I stop the wild zombie bears who are trying to murder me?

Every now and then while I'm scavenging, a "Boss Fight" occurs and a wild zombie bear comes after me.

I've never been able to actually kill it. I've either run out of time or been caught. Is it even possible to take a boss down? How many bullets will I have to use?

Solution 1:

It's not possible to kill the bear, only survive the encounter. When you shoot the bear, it will slow down. Kite it around (run away from it) until time expires. It will take quite a few bullets to escape, so if you're running low, it may be better to just take the hit than waste the few you have left. Also, when the bear appears, regular zombies stop coming (on Normal difficulty and below, at least - unsure for higher), making kiting possible.

This is from my own experience, shooting the bear pretty much the most possible number of times in the time allowed.