Sure it's childish of her to tell you something like that to get a rise out of you, but NT's by nature will do something more often if they know it will get an emotional response out of you. Simply ignore it and let her go about her business and she will stop informing you about it. Periods are a fact of life, remember that next time you get all "EEEEEEEW" about it. Remember that a woman gave birth to you and you owe your life to that vicious bloody mess.
On the subject of you being a gay man, this has nothing to do with the matter at hand. Straight or Gay men don't want to hear about it just as much as the other. So leave your sexual preference out of the equation unless it is immediately relevant. My brother in law and best friend are both gay, so don't bother saying I'm homophobic or discriminatory against homosexuality.
On the subject of it being (in)appropriate for the workplace, it depends on the context IMHO. Perhaps she initially said she was bleeding like crazy to give you a not so subtle hint that she wasn't going to use the restroom to blow off work, and only pursued it further because you made it abundantly clear that it bothered you. Remember as well that giving your boss the "He said/She said" routine, is something third graders would do and, won't net you any bonus points and only opens you up to retaliation if you do something that makes her upset. It's a give/take scenario and you should just take it at face value, she's being immature by looking to get a rise out of you, move along.
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Your Aspie score: 185 of 200
Your neurotypical (non-autistic) score: 16 of 200
You are very likely an Aspie
AQ: 49