Using cup in public washrooms

I recently moved into a university residence building with only public washrooms. Do you have any suggestions for using and cleaning the cup discretely without going into the shower every time?

That's a tough one. You can always bring a bottle of water into the stall to rinse it out before re-inserting, but I do like to wash mine at least once a day. If I was in this situation, I might have 2 cups. So you can empty one, put the already clean 2nd cup in, and have a small bag with you for the used cup. Hopefully you have a quick moment when you wash your hands to wash it discreetly, but if the bathroom is occupied, that way you can always come back in later to wash it when the sinks are *not* in use, or use the shower to wash it once a day. Some ideas for you at least.