The Nassau harbour also is a landing spot for seaplanes. I saw a seaplane of Chalk's International Airlines land and take off; but that company stopped in 2005.
You still can charter smaller seaplanes.
There are frequent direct flights from Miami and Ft Lauderdale to Nassau, there are also direct flights from London. Bahamas Air the national carrier of the Bahamas does offer inter island flights to Grand Bahama Island, Andros, Abaco, Inagua, Exuma, Eleuthera, Long Island, San Salvador, Cat island and international flights to Miami and Fort Lauderdale in Florida. You can also come by yacht to the Bahama's. In The Bahamas there is also the sea road fast ferry service between the island, check out my Travelogue above for more information on that service.
In Nassau there is bus transportation service however it is unreliable service and there is no time schedule, so busses come whenever they want. The best thing to do is to rent a car or a motor bike and if you not intrested in driving around just stay in the resort area.