I was just there and my wife and I brought our own bikes.

The state highway around the island is, well, a state highway so it's entirely paved. The best stopping point is the NW corner of the island.

Most of the roads are paved or very hard packed gravel. There are foot trails that are dirt that we rode on anyway because no one seems to leave downtown and venture out into the island, so you have the whole place to yourself.

Don't be fooled about not having motorized vehicles there. They are starting to allow semi trucks on off days of the week and before/after the tourist season starts (we talked to a farmer there who moves horses around a lot and says they just have to use 1st gear around the island).

It is actually a dangerous place downtown. Imagine a MUP with 1000x the traffic. Seriously. It was better for us to park our bikes and walk around town.

Also, no one locks their bikes there. They even have signs on the bike racks telling you that you cannot lock your bike (we found a few racks that would let us lock our bikes, though, but only two out of the whole place).

If you go to the island, go to bike around the state park. Downtown is pretty unimpressive.

You can even bike onto the runway at the airport. And you can bike into the wastewater treatment plant, too. Watch out for tourists driving their own carriages, though. That is kinda scary.