If I'm in the woods, I'd prefer to encounter the bear, over facing a strange, unattractive, and unknown woman. Whether you kill, flee, or cross on amicable terms with the bear, you're in the clear later, but there is no action you can do to be safe with the latter. Just the knowledge that you were in the woods at the same time, even if you never get within sight range, you're at serious risk forever after if she winds up feeling the need for some pointless facebook likes.