As others have stated:
1. pick your day carefully,
2. make sure that you have more than enough fuel,
3. have a mothership travel with you.
Even if you do this, be aware that you may have to ditch the jetski to board the mothership to save your life. NOAA weather reports predict sea state based on broad weather trends. If a supercell thunderstorm kicks up, there could be winds in excess of 50 mph and seas upwards to 8 ft around the storm. Generally, it rains everyday in Florida during the summer. Cross early as storms usually happen in the afternoon.
I once joined a flotilla from Ft Lauderdale to Port Lucaya on Grand Bahama in July. The seas were predicted to be 1-3ft. When I got up at 5:30am to do my pre-departure checks, there was lots of lightening and thunder offshore. The flotilla waited until 9:30am to depart. 10 miles out, in 6-8 ft seas, I turned around and headed back to port.
Also, I don't know how sensitive a jet ski is to fuel, but Mixman reported that his Honda outboards had a bad reaction when converting from ethanol fuel purchased in the states to non-ethanol fuel purchased in the Bahamas. The south Florida fishing forums also have reports of fuel problems when making the same transition. You can buy non-ethanol fuel at the marinas in Florida. It is more expensive. Perhaps you should run a tank of non-ethanol fuel thru the ski before you depart. If you have a fuel issue, are you capable of fixing it while drifting in the gulf stream? Lately, the gulf stream has been running about 4.5kts. The gulf stream is close to shore around Miami and 30 miles offshore by the time it gets to Cape Canaveral.