Hey, little lady!
I have never been bear hunting before so I cannot say what, if any, their reaction may or may not be. I, like yourself, have not noticed a bit of difference while out deer hunting and it being that time of the month.
I have, however, witnessed men wanting their wife's/girl friend's used tampon to use in the woods. *yuck*
In my honest opinion, it may draw the wild animals but only if used as we use estrus and like scents.
Hope that helps!
Good luck bear hunting should you decide to go. I would if I were you! I can't wait to be able to go bear hunting!