Always carry a beartrap around. You don’t even have to use it on bears, if you’re in trouble just drop it, wait until the enemy jumps into it and BASHBASHBASH.
That said, I generally kite them into bushes and hope to hell I can brain them with my crowbar fast enough.
Oh, always carry bandages too. Always Always. Normal zed attacks never seem to cause bleeding. Bear attacks seem to freakin disembowel you on the first strike though. Like they say, the fastest way to a man’s heart is through his stomach, under the ribcage and then through a lung.
After that it’ll be about 5 turns before you bleed out, depending on your torso health.