Several points to consider:
1. As others have said depends on where you want to go in Bahamas. For your first visit, would suggest the Abacos - are easier both in approach and in finding safe haven from cold fronts.
2. You’ll be going in winter when cold fronts pulse through every 3 to 5 days with winds clocking from NE to S, SW blowing hard to NW as the front passes and then to NE again. Your window to cross the Gulf Stream is when the wind is S during this cycle. It will take several days for the seas to lay down after a strong northerly wind. Wait for forecast 2’ or less seas. Expect to wait for favorable crossing conditions. (Referred to as waiting for weather).
3. All that said, would recommend going south from Stuart on ICW to Lake Worth inlet and wait for weather. Can either go to West End or to Great Sale. Suspect your crossing speed about 8 knots. Will need to aim about 16 to 20 nautical miles south as you cross the stream and let the current take you north (assume about 2k average current velocity). Return back to Florida can be from West End to Lake Worth or ride current north to Fort Pierce. Plan your passage through inlets in Florida for a flood (incoming) tide. Outgoing tides with wind opposing current make the inlets hazardous.
4. Get the Near Bahamas Explorer chart book. Can also get electronic version of Explorer charts for Aqua Maps. Acts as both a cruising guide and the most accurate charts.
5. We hope to get over to the Abacos in your time frame and then go south via Eleuthera to the Exumas. Maybe we’ll see over there!