A dog presents a real hazard to bicyclists. A dog can attack the bicyclist, or the bicycle, and cause a crash. An attacking dog can cause the bicyclist to swerve, running off the road into a ditch or into the road and a passing car. And, when you fall on a bicycle, particularly if you are traveling at a high speed, you will be very fortunate if you avoid serious injuries. (Clink on the link for more information about Tennessee dog bite or dog attack cases.)
Tennessee law provides that a dog owner has the responsibility to keep that dog under reasonable control at all times and to keep that dog from running at large. "Running at large" specifically includes a dog going uncontrolled on a public highway or street.
A dog owner who does not keep the dog from running at large is responsible for any damages suffered by a person who is injured by the dog if the dog is in a public place or lawfully in or on the private property of someone else. Liability is imposed in these circumstances even if the dog has never shown any dangerous propensities or whether the dog’s owner knew or should have known of the dog’s dangerous propensities.