My college roommate is sick of getting cat litter on her bed, advice?

I adopted a 1 year old short hair about a month ago as an ESA. I'm going through a rough transition and my psych and therapist thought it would be a good idea. I live in a college dorm, the set up is two twin beds on either side, desks, and two small built in closets. Outside is the bathroom and common room. Per university policy, she's not allowed in the common room or our bathroom.

My cat likes to sprint out of her litter box and get jump on the on things and run around like crazy and ends up tracking litter everywhere. My roommate confronted me about finding litter in her bed and that she's not comfortable with my cat having free range of the room while we aren't there.

She wants me to buy a playpen for my cat. My issue is that:

1.) It will further clutter up the room

2.) Being in an even smaller space for a long period of time may stress her out and cause her to act out. She's young and likes to climb and jump.

3.) The room is already so small there aren't many places to store the playpen when we put it away.

I suggested that she put up a screen pet gate around her bed since she has four posts around it. I also suggested spraying cat deterrent on her bed to keep my cat away, but she wants me to compromise and me do the play pen while she sprays her bed.

I understand that she didn't sign up for living with a cat, and she's been super paitent about the situation, giving a lot of grace. I tried to get a single room this year but had no luck.

Any advice on how to keep my cat off of her bed and keep her from kicking litter everywhere?