I'm perfectly happy with that idea and realize going further South is too ambitious to think about at this point.
Can you elaborate some on the feasibility of a complete noob 'gunkholing the Bahamas'?
Boat size, costs, training/learning for that specific trip?
A good friend of mine did almost exactly what you are trying to do with remarkable success. He had a bit more experience than you, though - one summer living aboard a Catalina 22. A couple of years later he and his GF quit their jobs in Massachusetts, drove to FL, and shopped around for a boat to sail the Bahamas. They settled on a C & C Redwing, 30' LOA but only 21' 9" on the waterline. The boat was pretty basic, stoutly built, the Atomic 4 ran well, the groundtackle was oversized and the mainsail was new. It was November 1991.
Both of these people are quick learners, able to come up with creative solutions, and were willing to accept a very simple lifestyle to achieve their dream. There were certainly times when they were very tired, cold, and wet. They lived without refrigeration, they caught fish with a Bahamian sling to supplement what was likely a beans and rice/noodles diet, and they learned from their mistakes. On one occasion they ran hard aground and spent at least the next two low tides creating a "channel" back to the actual channel by hand; the boat was so hard over they slept on the settee backs.
After seven or eight months I got a phone call. We've done it and had a great time, they told me, but now we need to sell the boat and move on in life. Where do you think we should sail to and sell the boat? When I suggested Annapolis they said okay. When they arrived I saw two exuberant and beaming souls who had gotten to know one another oh so well. They cleaned the boat up and sold it within three weeks for a profit; I think one of them was a very good negotiator and did well on the front and back end.
My friends married a few years later and continue today to raise a family in the DC metro area. I mention this simply because when the OP asked about "costs, training/learning for that specific trip" I thought it important to also describe some potential life-long dividends.