As a rule of thumb, Bermudians dress more formally than most Americans. Leave your cutoffs, short shorts, and halter tops at home. In the evening, some of the more upscale restaurants and hotel dining rooms require men to wear a jacket and tie and women to dress comparably, so bring a few dressy outfits. However, increasingly venues are more accepting of the trend toward "smart-casual." In this case, women should be fine with slacks or a skirt and a dressy blouse or sweater. Bermudian men often wear Bermuda shorts (and proper kneesocks) with a jacket and tie for formal events and business meetings.
During the cooler months, bring lightweight woolens or cottons that you can wear in layers to accommodate vagaries of the weather. A lightweight jacket is always a good idea. Regardless of the season, pack a swimsuit, a beachwear cover-up, sunscreen, and sunglasses, as well as a raincoat (umbrellas are typically provided by hotels). Comfortable walking shoes are a must. If you plan to play tennis, be aware that many courts require proper whites and that tennis balls in Bermuda are extremely expensive. Bring your own tennis balls if possible.
Bermuda-bound airlines commonly accept golf-club bags in lieu of a piece of luggage, but there are fairly stringent guidelines governing the maximum amount of equipment that can be transported without an excess baggage fee. The general rule of thumb is one covered bag containing a maximum of 14 clubs, 12 balls, and one pair of shoes.