The reason you're going to the Bahamas is to get away from all of that suit-shirt-and-tie turmoil, so your wardrobe should reflect the informality of the experience. Aside from your bathing suit, which will be your favorite uniform, take lightweight clothing (short-sleeve shirts, T-shirts, cotton slacks, lightweight jackets for evening wear for men; light dresses, shorts, and T-shirts for women). If you're going during the high season, between mid-December and April, toss in a sweater for the occasional cool evening. Cover up in public places for downtown shopping expeditions, and save that skimpy bathing suit for the beach at your hotel.
Some of the more sophisticated hotels require jackets for men and dresses for women at dinner. The Bahamas' casinos do not have dress codes.