Not all bats, a few species of bats, and it's technically menstration but different from "overt menstration" found in humans and primates.
Most mammals have an estrous cycle where the uterine lining is reabsorbed if pregnancy doesn't occur. If the uterine lining is destroyed instead, its menstration. Here's a paper that has an overview of the other mammals that have menstrual cycles and how they work.
I like the idea of you just sitting on your couch, suddenly looking around and slapping your knees to stand, just saying "WELP THAT DOES IT. I AIN'T LEARNING SHIT TODAY."
Some people argue that bats are primates, but I don't know enough about taxonomy to say. I do know that there was a defining feature for primates that had to get deleted from the primate definition because we found it in bats.
TL:DR : flying foxes' (those really large bats) brains are connected to their eyes in a similar way to primates, but different from all other mammals (including smaller bats). Though apparently this theory doesnt hold up when comparing the DNA from flying foxes with small bats and primates respectively.
I was in my parents' yard once and something wet fell on my head. I touched it and it was blood red. Totally thought I was bleeding until I noticed tiny berry seeds in the substance. My grandma said that happening to me meant I'd have good luck.