Menstruel cup at university-how?

Hello! I'm leaving to go to uni in a few days and this might be a stupid question but, in regards to full floor public toilets and all that, how do I deal with my menstruel cup? It needs to be washed, and I'm not sure how best to do that in a public toilet setting, since I'm assuming there won't be any single toilets with a sink anywhere nearby. I don't want to make anyone uncomfortable but I have to consider hygiene, so, thoughts?