Take a sea plane from Miami... I flew Chalk 's Ocean Airways. They fly out of both Fort Lauderdale and Miami and can be reached at 1-800-424-2557 for details and schedules.
The main island (North Bimini) where all the hotels & bars are located is so small, you can walk everywhere. I think the widest portion of the main island is 700 to 900 feet wide and around 5 or 6 miles long.