Well, if I were in space for 3 months, I would sure as heck not want to deal with the whole mess. I wouldn't be surprised if the women astronauts used Depo-Provera or something like it to manipulate their cycles. On the other hand, prolonged weightlessness leads to bone loss, and the absence of a normal menstrual cycle also leads to bone loss... so maybe suppressing the menses ain't such a hot idea.
As far as your original question, Alex, gravity is part of the process but not all. The non-pregnant uterus isn't very big, and liquid would find its way out eventually even if we all hung from gravity boots during our periods. Which would, I suppose, be an interesting test.