This sounds just like my Lilly. I got her when she was about 9 weeks, she peed on EVERYTHING until I got her spayed at 11 weeks.
Ever since she’s been spayed her litter box habits have improved DRAMATICALLY! She’s not perfect but she’s a lot better.
I’ve found that starting them out in a small area with a corner litter box (after neutering/spaying, cause otherwise they are more likely to mark everything with their “scent” (pee)) gets them used to using it all the time. It takes a lot of time and patience, but worth it IMO.
Lilly was honestly aweful haha, but I got her this big pop up play pin on amazon 55″ diameter and put her litter box in the corner she had been peeing in. You also have to put allllll the poops in the liter box along with a paper town with her pee on it. It works well.
I also got this stuff you can sprinkle in the litter box that’s suppose to help train them.
Anywho, once you train them in that small area, get them netured, your bun should be good on the bed. I would put down another blanket just in case she has a accident and always have a small cage or litter box on the bed with you at first. That lessens the chance of accidents.
Hope that helps!!!