Period blood does not attract bears.
Bears that are in America such as black bears, brown bears etc are not attracted to a women's period blood any more than it would be attracted to other human blood.
A woman is safe going camping or near bears when they are on their period.
The smell of the period blood is of no interest to bears.
Well that is for most bears.
I've heard that Polar bears are attracted somewhat to period blood.
But most other bears are not attracted to period blood and as long as you leave the bears alone and keep your distance from them and keep your food put away from the bears then you'll be okay.
I've been near bears while camping when I was on my period and even threw period pads away that had period blood on it and the bear didn't even bother the bloody period pads.