Unless you are dealing with Polar bears the answer is: No.
According to an article on livescience:
Despite campfire fears dating back to at least 1967, black bears and grizzly bears are not attracted to the odors of menstruation, according to a recent Yellowstone National Park report.
Polar bears may be interested in the smell of menstrual blood, the report found, but bears that roam in North America are not. Food is a much more important temptation for bears, according to the findings.
They also add
[According to a Yellowstone Park Report] the report concludes, there is no evidence of a link between bear attacks and menstruation. Nevertheless, the Park Service recommends using tampons instead of external pads and unscented menstrual products to keep potentially appealing odors down.
The Yellow Stone National Park Service has an article from 2016 dedicated to this subject. Citations can be found on that page.