The cheapest week long liveaboard is likely Blackbeards at $939 + $100 in port fees/taxes etc. They leave out of Nassau.
Blackbeard's Cruises Liveaboards, Bahamas scuba diving
Sometimes their affiliated catamaran - Cat Ppalu sells unused charter spaces for $1545 + $100 f/t. The advantage would be a semi-private cabin instead of what's been called camping at sea on BB...
The Cat Ppalu is normally charter only, but a few of the groups sometimes have space that we can fill. If you have a interest in a particular date, please contact us and we will check with the group that has that date booked.
Lost Island Voyages is Cat PPalu's competition. They also leave out of either Nassau or Freeport, Grand Bahama. I'm fairly sure they're similarly priced, at least they were the last time I checked. They also sell extra spots on their charters - I think they have some open boat weeks also.
Carib Dancer is $1795 in the Quad bunk cabin - there's only one. They've had some problems lately including cancelling this weeks trip so do a search here about them. You'll probably see reef sharks and maybe hammerheads - my buddy did. They also leave from Nassau.
For Tigers - and Lemon Sharks - it's JASA - Jim Abernethy's Scuba Adventures Tiger Beach trips.
Bahamas & Palm Beach, Florida Scuba Diving :: Jim Abernethy's Scuba Adventures IIRC it's over $2K. It's shallow water diving but you get up close and personal. An advantage from Dallas is a Florida departure. Search Tiger Beach on Youtube for examples.
Or Dolphin Dream - they also go out to Tiger Beach. They have some interesting shark trips this spring:
Book a Trip on board the DOLPHIN DREAM. Cruise the Bahamas for a week. Some (all?) of their trips leave from West Palm Beach, FL.
You can also get out to Tiger Beach on a day trip basis from Grand Bahama - Stuart Cove's has a facility there doing that now. Long boat ride from there though. You might look at staying somewhere reasonable part of the week (Bell Channel Inn is one option) doing some local diving - UNEXSO has both shark and dolphin dives then going out with Cove's.
Another option from Dallas might be Sun Dancer II in Belize. It's $2195 + fees but they have two trips in August where you get 10 days for the price of 7. The other advantage it has for you is that you can be there by 2PM on AA and the return is a direct flight. They'll pick you up so your only expenses would be the crew tip and dinner Friday night.
Aggressor and Dancer fleets post trip reports in their forum so you can get an idea of what they're seeing.
Aggressor Fleet and Dancer Fleet
Spree also has a forum here. [user]Wookie[/user] owns it.
Any of the Bahamas trips you might see Hammerheads - Reef sharks are common - they have been every time for us.
Also get in touch with Explorer Ventures (call Mary...) They used to offer discounts of up to $500 on some of their trips during the year - usually they sent out an e-mail - and they book up fast - usually within a day or two. We did a week on the Turks/Caicos Explorer that way - a $2295 upper deck stateroom cost us $1795 plus $200 fees/fuel surcharge. Lots of reef sharks, rays etc. What to expect - thanks to Mike Southard:
Saudio's Trip Reports
They also have lower deck cabins at $2095 so with the discount that gets close to the Bahamas trips pricing. They also have availability this month and next on their NE Caribbean trips at $1395 but they go to Saba/St. Kitts which is more smaller stuff from what I've been told. It's also less diving intense - they do optional island tours etc.
Unless ocdiver knows something I don't you're also looking at a lot more for Socorros trips. Rocio Del Mar is $3195 and sold out in 2013. Solmar V is $3295. Nautilus Explorer is $3150. If you can go 1/17/2013 they have one space available at $2495. That would hit all your shark species at once - including Whale Sharks and about a dozen others you didn't mention - not sure about Tigers but huge schools of Hammerheads are common there.
White Sharks would be on Solmar V out to Guadalupe Island. They're cage dives and surface supplied air only. Also expensive. One of the San Diego boats also goes out there on a charter basis thru one of the White Shark dive outfits.