Cougar Bait

There have been a number of cougar sightings in our community lately. None were very close by, but at least two were within about 5 miles of my house. An acquaintance (who got to listen to a cougar snarling repeatedly at 4-something a.m.) mentioned in passing that cougars will attack a menstruating woman. So, when I fit that description, do I stick to my treadmill? or venture forth with my trusty (though concealed) pistol and hope to reduce the cougar population? I'm not sure I'm a quick enough draw for the task, particularly as I usually don't have a round chambered.