Is my Suitemate just very difficult to deal with or am I being a jerk?

I agree with @auntbea. I would take my own roll of tissue when I go into the bath. I really wouldn’t be so concerned about whether she is satisfied with my cleaning or not because it seems that she is very insecure. I would clean my side and clean prior to using and behind myself. As far as her coming into my room, I’d probably make it clear that I want to have a civil relationship but am asking her to not come uninvited.