Here's a semi-complete list of boats that have dove somewhere in the Bahamas. Some may/may not be going to the Bahamas currently. Some may also be boarding in the Bahamas only now.
MV Spree - going to Cay Sal this August - if I could I'd be on it. Not much of anybody has been down there in about 6 or 7 years. Since it's on the way I'm sure they're stopping at Bimini also. It's the south Bahamas - Cay Sal is near Cuba but good blue hole dives.
Dolphin Dream - out of West Palm Beach
Shearwater - Abernethy's boat (JASA)
Easy Goin'
Playmate
Ultimate Getaway
Add in Nassau/Freeport departures since it's a short cheap flight from MIA/FLL to Nassau or a ferry ride from FLL to Freeport.
Lost Island Voyages
BlackBeards
Aquacat - the biggest, arguably the best on this list.
Carib Dancer - the Agressor Fleet boat.
Cat Ppalu - full charter but occasionally sells extra spaces
MV Juliet - IDK their current status.
Blue Iguana - MV Kate - may have gone private only this year - IDK. They don't list any current 2014 departures except private charter options.
Additionally better diving with the same extreme walls is Turks/Caicos. Fly into Providenciales, there's both an Aggressor and Explorer there. We did the Explorer, clear water, lots of sharks. 6000' deep walls. Some years the Turks/Caicos Explorer moves over and dives the Bahamas also - it doesn't look like they are for 2014-15.
Reply here if you have trouble finding any of these and I'll provide websites/booking agents.