I would try to have a talk with her about your schedules in the bathroom. I would also ask her to contribute to toilet paper and cleaning materials. If she says no then I would let it go and bring your own TP when you go to the bathroom and see how long she will last.
My daughter is sharing a 2 bedroom with a nice apartment mate. She is lovely, except bad at cleaning the bathroom, so my D cleans it to the way she likes it. Your roommate isn’t lovely, but I would still just clean and not expect her to do it (it’s not worth it).
As far as your roommate coming to your room uninvited, I would keep your door locked except when you go to the bathroom. Don’t let her in even when she knocks. Just because you share a bathroom it doesn’t mean you need to be friends.