If sorting out an FAA IR turns out to be too much hassle and you really want to tour the Bahamas then you could always fly to Nassau commercially (flights are pretty cheap from Miami and Orlando) and rent a plane there without an IR. I rent regularly from
Welcome to Prestige Air Ltd. - Prestige Air Ltd.. The planes are older Cessna 172s but I haven't had any trouble with them and the guy who owns them is happy for them to be taken for overnight trips. At least it gives you the chance to see the (spectacular) Bahamas even though you don't get to fly there yourself.
Having said that, it's that time of year now where there is a lot of rapid cloud build up without much warning so an IR would be a good thing to have. My own flying has been curtailed over the last few weeks as I don't have an IR and I never know if I am going to be able to get home if I go to one of the other islands for the day.