I just adopted a 2yr old male bulldog. His first owner crated him for 12hrs a day, then he went to a foster home with a female bulldog. He went to his new home for 2-3 days where they had 2 jack russells that attacked him. Now he is with me.He came home with me on Sunday. No accidents in the house. We went to the vet on Monday, he is in excellent health. He did get a rabies shot. Yesterday after we got home from the vet, he laid on the kitchen floor to sleep and peed himself. I was wondering if this could've happened because of the shot and maybe being tired. Later in the evening he jumped on the bed, where he slept the night before. While on the bed he crumpled the blankets as if he was going to lay down but instead, he peed. I immediately ran him outside. Not even 30 minutes later, he did the same thing. After that, I refused to allow him on the bed and made him sleep elsewhere. Knock on wood, no more accidents. Is this a dominance thing? What do I do?

The first thing that needs to be done is to rule out medical issues.
A routine exam doesn't normally include blood work and other things, but rather a good look and listen.
I would suggest having a urinalysis done to check for urinary tract infection and go from there.
Also, is he neutered or intact?