Generally, this kind of behavior will take place after a stressful event. It is very common after a dog was scolded. This is why many dog owners think that their pet is being spiteful. The truth is the dog is very upset and vulnerable and when a dog is in that state he is more likely to make himself feel better by peeing in your bed.
Some dogs are more submissive than others. Very submissive dogs, shy dogs that lack self-confidence and often young pups will urinate when in the presence of more dominant dogs and humans.
Many dog owners mistakenly believe that this type of urination is a housetraining problem, and try to correct it with discipline. But scolding a dog who has peed on your bed will only make the behavior worse! Because the message he's sending is misunderstood by the owner, the dog is caught in a vicious cycle - his instincts tell him to urinate to please his superior by showing submission. But when he does, he is punished. He then tries harder to please by urinating even more. This results in more punishment, and still more urination. After a time, the dog may become so confused and insecure that he urinates at the mere sight of a human being or another dog.
I would just give him a lot of attention and love and try to take him out often and when he pees outside, praise him a lot. I think he is intiminate by the other dog but patience will help him.