Bermuda is generally, and relatively speaking, a safe destination. There have been incidents of theft such as handbag/rucksack snatching (either on a person, bags left on the beach while swimming, or snatched from a rental scooter basket while riding). Break-ins are becoming more common than they used to be, with small guesthouses being the prime target. Just use your normal precaution as you would anywhere. With the earlier exceptions, visitors to the island are not targeted in other areas of crime; more serious crime is between Bermudians.

Regarding safety on the roads, something to keep in mind while in Bermuda: don't plan to walk any distance on roadways. For the most part, shoulders are narrow at best. Visitors who rent scooters should read up on motorcycle safety before visiting and should drive defensivly.  Bermudian traffic moves quickly, and scooter accidents are serious and common though more locals are injured than tourists.  If taking a bus, and it's during the summer, look closely before boarding. If windows are open, or people are fanning themselves, the air conditioning isn't functioning. Wait for another bus.