Bermuda is a beautiful, safe island and you can find lots to do...however what you might not know is how long it would take to get from one place to another.  Yes, buses run on the main roads, and no, you might not want to rent a moped unless you have some experience and don't mind very fast traffic and crowded main roads.  However, walking to various bus stops and waiting for buses takes up a larger chunk of the day than you might imagine.

Buses are clean, air conditioned, and people are friendly. And while the island is only 22 miles long, it will take easily an hour for the bus to go from end to end.  Managing the schedules is a big task.

Also, the island is very hilly.  Biking would be a challenge if you could manage it on narrow roads with no shoulder at all.

Walking is a challenge at times even if you are reasonably fit.

If you only have a few days and want to see lots of places on the island, perhaps hiring a private car/driver would be worth looking into.