Having made this trip many times, albeit in a MUCH MUCH larger boat, I can tell you it can be VERY rough. I have seen where there is a 2-3' swell at Miami and 6' waves when you get to the Gulf Stream. You really have to pick your time if you are going in a small boat.
From Ft. Lauderdale the closest point in the Bahamas are the Biminis. All the marinas are on the east side of the islands. Your trip is really around 60 nm or 65 mile. From there, any other island is at least another 60 nm.
The reason most do it on a jet ski is that if you get swamped, you can get back on and go. In a boat, it is very different. These boats are not made for ocean crossings. If you are not use to blue water boating, it can be very dangerous.
I suggest you practice boating near shore in the ocean for a while to see how your boat handles. One wave on the beam and you could broach or swamp. I also suggest you take a safe boating course from the Coast Guard Aux. or the Power Squadrons.
Since you have to contend with real waves, you will not be doing 50mph. More likely something below 30mph if you are lucky. Slower is often better. Three hours of pounding and you will be very tired. In addition, you will find that you can not go in a straight line. You will have to tack a little to take the waves on the quarter, this will increase the distance and fuel usage. Be prepared to get very wet. If you try to go too fast or don't read the sea correctly, you will get into trouble.
I am not saying it can't be done, but you had better be prepared.
Make sure your boat is in top condition. Leave early in the morning, you do not want to be traveling at night. Have a waterproof vhf radio or two and know how to use them. Cell phones don't always work and the Coast Guard does not monitor them. Wear a type I or II pfd. The little type III jackets will not cut it if you go in. Have a GPS so you know where you are and where you are going. Get a nautical chart and know how to read it. Plot your course before hand and use waypoints. Make sure you have plenty of drinking water, extra fuel, oil, and food. Make a float plan and leave it with somebody on shore. Make sure everything is tied down, you do not want a gerry can of fuel banging around your boat.
DO NOT try this alone. If you can't get other boats to go with you, hook up with a large yacht and follow them. Most captains wouldn't mind and their passengers would probably find it interesting.
This could be a cool trip, if you are prepared.