For private pilot students I'd be very careful in the Bahamas, not only over water ops, but these places can be crazy busy with vfr traffic and airline ops. Especially since a lot if non standard things happen there it can be dangerous.

Most fields are uncontrolled with the exception of Fpo and NAS. Like mentioned I would probably save those trips for your commercial ticket. Remember you also have to comply with over water requirements as well as customs paper work.

Fly safe and have fun!