Do you have a current passport from your naturalized country?
Is your green card current?
Going to/from Bahamas is a pretty easy process for legal US residents, that said contact the cruise line (and if you get someone that says "you need to contact your travel agent or some other agency, they just don't know the answer, cruise lines deal with this day in for every cruise, they know what it takes to get "you" on the ship so don't accept a doh answer) to confirm that they will accept the documentation you have
"PLUS" without a passport you will also need a "certified" birth certificate, in the US we call it a "raised seal" meaning it has to be certified by your state or county of birth or
in your case maybe country whatever constitutes a legal document for you, or you can contact the US Department of State.
One thing to keep in mind, if you get on the ship, and something goes wrong, really wrong, you would need a passport (from some country) in order to "fly" back to the United
Again that said, do your homework and make sure the duck are all lined up, usually a Bahama cruise is a 3 or 4 day, not good sitting in Ft Lauderdale for 4 days saying "wish I was there"
As far as directly answering your question I am sure that I am not point on, I am a natural born citizen with a current US passport so they damn well better let me back
in even if it is on a refugee boat, meals not included I'm sure.
Hope my thoughts help and you get to have a great cruise experience............