Harry Finley, director, opened the museum in 1994 and ran it from his basement in Washington, DC, every weekend until 1998. He was the sole director, curator, and employee. It exists at present only on the web in a very comprehensive form at www.mum.org. You can readabout why he closed it, if you're interested. This site is very personal with a lot of editorial notes. There is a touching letter to the public from Harry Finley about his mother, for example.
This appears to be (probably) the only museum in the world about menstruation. It touches on health issues, but the focus is mostly cultural, with as many examples of items and information from different countries (for example, an exhibit in Norway) and time periods as Mr. Finley could gather. There are pages on old fashioned items as well as newer technology, jokes. There is a video tour on the site as well as a photo tour.
Although the museum is not currently open to the public, I think that the web site gives a good idea of what the museum was like. It is still in his basement and he has plans to open it again some day.