If you are IFR capable and your aircraft can fly at 12,000' or above you do not need to stop at the nearest airport of entry when coming back to the US. If you are neither of those then you must stop to clear customs at the nearest airport with customs. I have been to Ft Pierce and can say that when we were there they were courteous and professional. You can get the information you need directly from the Bahamas tourism website describing the procedures and don't need to buy a book for $34.95, although it is a nice book. The Bahamian tourism ministry also often run deals to reimburse for avgas if you stay a certain period of time in country on the islands.
https://www.bahamas.com/getting-here/private-aviation
Things to note:
You must file an EAPIS for your flight inbound and outbound
https://eapis.cbp.dhs.gov/auth/login.html?resource_url=https%3A%2F%2Feapis.cbp.dhs.gov%2F%3Futm_source%3Dwww.faa.gov%26utm_medium%3Dwww.faa.gov%26utm_term%3Dundefined%26utm_content%3Dundefined%26utm_campaign%3D%28not%2520set%29%26gclid%3Dundefined%26dclid%3Dundefined%26GAID%3D1748466594.1609484072
No night VFR in the Bahamas.
You can buy a US customs sticker for the plane before you leave (takes weeks to get in the mail) or pay a fee at customs when you get back sans the sticker.
https://dtops.cbp.dhs.gov/main/#%20
File a plan leaving the US.
Arrive at airport of entry in Bahamas and get a cruise permit.
Fly from island to island and enjoy the scenery.
Depart from airport of entry from Bahamas and pay fee.
Make sure to file a plan coming back to the US and establish radio contact before crossing the ADIZ.
Land at nearest US customs airport and clear customs OR fly at 12k on IFR plan to customs airport of choice.
https://www.faa.gov/air_traffic/publications/us_restrictions/airspace/
Our favorite place to stay in the Exumas is Staniel Kay. The Chamberlain cottages are competitive for the island and have nice accommodations. Rent a 17-20'ish boat and you will take yourself and wife to many of the things to do while there. Google will tell you all about them but the Bond Thunderball grotto is there, swimming pigs, iguana islands, a few aircraft crash sites, etc. all only accessible by boat.