Are you docking at the Royal Naval Dockyard? If so the rental place is just a very short walk from the ship and than if you rent for 2 or 3 days you can even park them right in front of the ship..how easy is that one. It is like parking in your driveway when your coming home !! I can't tell you the prices but I saw nice fancy scooters to very basic plain ones.
Google Oleander Cycle rentals in Bermuda and that will get to them, also right there is jet-ski rentals too. What a place to do everything. Penny is correct, right there on the Dock is the place to get your bus/ferry pass $12 a day....so easy to get around. I JUST LOVE BERMUDA ! Going again in May whoo hooo