Folly...as a former owner of a Cat22...let me say that what you are planning is in my opinion quite risky and I do not think it is a good idea. I hope you take a life raft
with you. Not saying it can't be done...just that the degree of risk is high. That said...if you ARE determined to go you have two choices:
1. Leave from south of Miami (NoName Key) and cross to Bimini for check in ($150 for 6 mo. cruising permit). And then work your way to Chub Cay and down through the Exumas.
2. Leave from West Palm Beach/Lake Worth Inlet and cross to West End Grand Bahamas for check in and then proceed to Great Sale Cay and the Abacos chain. (recommended!) Cruisers anchor
at the north end of Lake Worth and wait for the right weather and then tend to move closer to the inlet as they get ready to cross, often in a group. You cannot expect anyone to cross with you since you will be so relatively slow...but at least you will have folks in radio
range...assuming you have a full power VHF
The check in process requires a passport and your boat registration and $150 for your size boat. Raise a yellow Q flag and hail customs and immigration on channel 16 as you approach either harbor and they will give you instructions. Have a Bahamas cruising flag to raise after you get checked in as they tend to take this seriously as a matter of respect.
There are EXTENSIVE threads here about crossing the Stream and cruising the Bahamas. Use the advanced search function above and enter Bahamas as a key word and my screen name and you will find a lot of them.
My advice...explore the KEYS in your Cat22 and wait for a more sea-worthy boat to tackle the Bahamas. But good luck in whatever you attempt.