We lived on MDI (Bass Harbor) for 4 years when I was a kid and I rode my bicycle everywhere (dated a girl in Bar Harbor 18 miles 1 way). Definitely take the Island Explorer or rent a car. Most of the roads are not made for large RV's.
I still remember the time a big tour bus ran me off the road; somehow I managed to get my feet out of the toe clips, bailed off the bike and landed on my feet. 40 years on I'd be a mess on the side of the road.
MDI is great and lots to do and see. The park loop drive is beautiful, Thunder Hole, Bass Harbor Head, Cadillac Mountain, Jordan Pond House for popovers, lots of carriage trails for hiking or bike riding. There used to be a park service nature cruise out of Bass Harbor that was quite good. If you're into sailing/yachts, Hinckley is in Southwest Harbor and Morris is in Bass Harbor. If it's hot, locals go to the bluffs at Echo Lake for a swim. Bar Harbor and Northeast Harbor are upscale, Southwest Harbor, Bass Harbor/Tremont (referred to as the "backside") are less touristy, more rural and traditionally where the majority of year-round working class folks lived. Which is why we lived there too!
2012 GMC Sierra 3500 Crew Cab, Long Bed, 4x4 Dually
2010 R-Vision Trail Cruiser 23QBC
2001 Catalina Capri 22 sailboat "Verboten"