Weather forecast for the Gulf Stream:

Friday Night
Southeast winds 10 to 13 knots. Seas 2 feet. Intracoastal waters a light chop.

Saturday
South winds 10 to 13 knots. Seas 2 feet. Intracoastal waters a light chop.

Saturday Night
South southeast winds 10 to 13 knots becoming southwest 9 to 12 knots. Seas 2 feet. Intracoastal waters a light chop.

Sunday
Along the coast...west winds 7 to 10 knots becoming south southeast 5 to 8 knots in the afternoon. In the Gulf Stream...west northwest winds 11 to 14 knots becoming south 5 to 8 knots in the afternoon. Seas 2 feet. Intracoastal waters a light chop. Isolated showers.

Sunday Night
South southwest winds 8 to 11 knots. Seas less than 2 feet. Intracoastal waters a light chop.

I think your plan is a sound one, Jan. I've crossed the Gulf Stream many times, thought I leave from Biscayne Channel just south of Key Biscayne, and have a little faster boat. Went over last weekend (Thurs night) in about a 13-14 knot wind dead ahead from the SE, and had to take a more southerly tack to keep wind in the sails and so we were fighting the stream and bashing a bit and it took me longer than normal. Leaving from Rodrigues Key which is about 20nm south of Key Biscayne, you should be able to maintain a more easterly heading and not fight the stream. You'll be in the main part of the Stream about 10 hours which will push you about 30nm north, so leaving Rodriguez with an easterly heading ought to about do it to pull into Bimini. I wouldn't want to sail that tack with a strong east wind, but with a S or SSE or even SE breeze forecast for this w/e you should be able to maintain course towards Bimini on a nice tack, and with good conditions in the Gulf for a great overnight sail.

Bimini is a nice and friendly place to check in, and since it is farther north than South Rock, you can take a less southerly heading to make landfall. You can hang out a day in Bimini if you want and then head out the next morning to cross the Bank towards the NW passage and on to Nassau and the Exumas.

Watch out for the Freighters and Cruise ships in the Gulf, you may see a lot of them, especially in the first 1/3 of the way over.