Firstly you need to get the FAA piggyback license on the basis of your existing one.
Then you need to do a biennual flight check with an FAA instructor.
As to FBOs nr MIA try ADF out of KTMB SW of Miami around SW 152 seem a bit more professional than Silver Express on the same field.
A bit further south is Homestead General - X51, smaller an less time wasted taxing about. Orient Flight seem to be pretty good.
As to the Bahamas, you need to check if the latest security malarkey will allow you to travel that route without a full US visa.