If you are in areas in the Bahamas that have cellphone service, you can use your Cellphone, however; it's very expensive. One way to redue this costs is to have your phone unlocked and then use a Bahamas SIM card. Costs are much higher than in the US but considerabley cheaper than using your own carrier. $0.49 per minute to call anywhere in the US.
As far as internet is concerned WiFi is available in many areas and most of the time it's free.