what I used to do was well, to be honest i didnt DO anything.. i just changed my attitude to 'i dont care' i remember i used my exboyfriends dorm bathroom and accidentally got blood on the toilet, he thought it was hilarious and told me to write on the walls with it. haha (i didnt)
use tampons and you can flush them down, use the trash cans if no one is there, and if someone is there, just put the pad on the back of the toilet seat. chances are you will never visit that bathroom again, and the other person in the room isnt going to look in the stall after you are done, and anyone who sees it will just think a girl somehow went in there by accident lol. just get out as fast as you can if you do leave it on the toilet.
if you are the type of person who would feel this is rude.. then I suppose you coudl take a little baggy and put the trash in that and throw it away in a different trash can, ball it in your hand so no one can see it
btw, i thought you were on T, how did you do the facial hair?