any idea why does my cat pees on our bed?

She is probably trying to mark her territory from the new addition. She is probably peeing where she smells the other one

Cats are also creatures of habit. She may have peed there the first time because she was upset about the new interloper. After that she'll do it again and again because she smells it there. Our Persians were really bad that way.

I'd say she is trying to tell you she is pretty pissed off about the new addition.

Don't forget to take her to the vet to get checked some may have a bladder infection as well making it hard to get off the bed going to the right place, Otherwise it could be certain smells anything with amonina in it certain perfumes or scents that the cat maybe mistaking at a territorial marking of the new one.... if it's a male that maybe it too just them claiming the area as theirs... - DNatureofDTrain

Sometimes if a cat has a urinary tract infection they for some reason do exactly what you are saying your cat is doing. I have a cat and for some reason he would constantly pee in the same corner all the time. I would clean the carpet repeatedly and no matter how well i cleaned he would continue to pee there. Come to find out he had a urinary tract infection and the vet said that when cats get that they will find a place they like and pee only in that spot. Weird I know but I am guessing it is true because after my cat got rid of its urinary tract infection he quit peeing in that spot and started using his litter box again.