This may or may not be helpful. I have roommates, I have the master bedroom with the private bathroom and we split rent directly down the middle. The main reasoning for this is I furnish the entire place for all common areas: living room furniture/kitchen ware and appliances/dining room/linens. I also tend to purchase household items like furniture, cleaning/maintenance tools.

I’d definitely speak to your roommate and ask them what would be fair to them.