If you get a bullseye rash at the site of a tick bite that means that you (or in this case your dog) has been infected with Lyme's disease. Lyme's disease, if left untreated can become a very very serious issue and result in all kinds of permanent damage to the various organ systems of the body and even to death. Dogs are especially sensitive to Lyme's disease. If its caught early it can usually be treated without much of a problem. If your dog really does have the bullseye rash you should get to a vet asap to get it treated. Also if you suddenly develop any symptoms or new medical problems, tell your doctor that you think your dog was infected with Lyme's disease. Trust me this isn't something you want to fool around with for too long, the damage it does is irreversibly permanent.