Yes! American currency is accepted in The Bahamas. You will want cash for the taxis, car rentals, bars, ect. Most places do take credit cards but cash is usually desired.
Your passport, drivers license for renting a car, bug spray (the bugs can show up on the beach every now and then), bug bite relief cream like cortisone 10, sunscreen, lightweight long sleeve shirts and long pants, any snorkel gear you may have, insulated water bottles, beach bags, phone chargers.