kainebob...so many times, I have crossed from Miami to Bimini in the last 47 years with different boats.
First, with your Grand Banks, you can get under the fixed bridge at Haulover, North Mami. Look it up. Second, there is an excellent anchorage at FIU (Florida International Unisversity). Actually, the anchorage is in the Oleta State Park. Protected from ALL wind directions, and holding is excellent. Gadabaut will wait here, as you can dingy ashore, bike trails, dog walks...etc. Anchor and wait for a weather window (previous poster is correct..do not go with ANY component of North wind.) You now have two options.
One, you can go under the Haulover Bridge...32 feet clearance...and head for Grand Bahama, and help with the Gulf Stream, or crab in the Gulf Stream current for Bimini. Both I have done. No problem with a GB.
Two, if you see a weather window, a couple of days out, you can travel down the ICW to Cape Florida, and No Name Harbor (again look it up, busy place on the weekends, but a nice Cuba restrauant), and wait there to cross from Cape Florida (south end of Key Biscayne) to Bimini. Less of a crab angle on the stream. Watch for a yellow buoy on the reef line, sometimes hard to see, and dead on course to Bimini inlet...go figure..almost hit it once while I was down stairs getting a beer.
Two places that I like to check into in Bimini is, Bimini Blue Waters, at $1/foot. Electricity and water extra. You can walk from there for the check in proceedures, aka customs and immagration. The second, is Bimini Sands, which is straight in from the enterance channel to Bimini proper. (Again look it up). However, with Bimini Sands, they now charge $2.50 a foot, used to be $1.50, and you will have to take a taxie to the airport to check in.
BTW, at Bimini Blue Waters, the liquor store is just out the front gateto the left, and down the street on the right. You will need to buy something to celebrate your crossing......just my two cents worth.
From Bimini, you can leave early,early to travel around North Rock towards Great Harbor, or go down to Gun Cay, bank side, and anchor. Leave at midnight to cross the bank and arrive at Chub Cay in the morning hours. That is a 75 mile run. I understand that Chub is now open, and I think they are pricy....(Again look it up on Explorercharts.com they have dockage pricing info.