I haven't done it, but one time that we stayed on Bimini, we saw 2 ladies who had gotten bikes up on the north end (we came over on the FastFerry from Fort Lauderdale), and I swear we saw them at least 3 times in one day, all over the island.
I've only even driven a golf cart on the island, but if you're up to the ride, I think it would be pretty safe. The majority of vehicles on the roads are golf carts and and a some mopeds these days, so traffic can't go all that fast.