Downtown Bar Harbor is best walked — it is only about ten blocks square. For everything else, use the Island Explorer, the free propane-powered bus network that runs from late June to mid-October and connects the town to all the main destinations in Acadia National Park, as well as Bass Harbor and Northeast Harbor on the other side of Mount Desert Island.
Parking in town is metered, scarce, and policed. If you have a car, the simplest plan is to leave it at your accommodation and use the bus. Bike rentals are easy to find on Cottage Street; the carriage roads inside Acadia are flat gravel and built for them.