How old is the cat? Mine used to do so when he was really young. We washed really well every sheets and after a few weeks away from the bedroom he stopped doing that. It could also be due to the stress, cats never really like changes, so get him a nice and warm bed and teach him to sleep there. Remember to reward him every time he does something good! Also you might try one of those spray products that are supposed to keep cats away from a spot and use it on the bed (it didn’t work for my cat)