The narrow body of the flea maneuvers the fur-covered bodies of animals. Its hard shell doesn’t crush easily. This is an example of a parasite that lives on its host. I have squeezed fleas between my fingers, only to have them jump out of my hand.
Bed bugs are not designed to live on their hosts. Their horizontal, soft bodies are quite the opposite of fleas. This family of parasites feed on their hosts, then duck out for a few days while they digest.
Oftentimes, they will not even crawl on you to bite. Usually, they perch themselves on their hind legs, feed, then recede to a safe crevice. Bed bugs will sandwich themselves between two objects to protect their soft bodies.
This is not to say that you won’t find bed bugs on pets or people. By all means, they are hitchhikers. That is how they get around. In extreme cases, they will begin to live on people. Pets too in this matter.
In most cases, you will not find bed bugs infesting pets. Bed bugs are host specific. They need to be feeding on human blood to thrive.