Bus routes radiate out from Rhodes Town to destinations all over the island. Only along the northeastern shoreline between Rhodes Town and Lindos, though, are services frequent enough to be truly convenient for visitors.
If you want to explore the island as a whole, it's best to rent a vehicle of some kind. All the major car-rental chains are represented at Rhodes airport, and plenty more car- and motorcycle-rental outlets are scattered throughout Rhodes Town and the resorts. Competition is fierce, so shop around.
And bear in mind too that if you're only visiting Rhodes for a few days, perhaps as part of an island-hopping itinerary, there's plenty to see in Rhodes Old Town without venturing further afield.