Andros is wonderful - one of my favorite dive spots in the Bahamas - NIE! - in the whole world! It has a lot to recommend it, not the least of which are Jeff and Mike at Small Hope are two of my favorite dive leaders/resort operators anywhere.
But it isn't what I would classify as "cheap" - although your definition of cheap may be different from mine. Small Hope easily costs $330+per person per night including accomodations, diving, meals. Not including if you do extras like the shark experience dive, bonefishing, etc and gratuities for dive staff. Then you have to actually fly to Andros in the first place - which means a plane ticket to NAS or FLL, then another plane ticket of $150-250 pp on either Western Airlines or Continental Connection.
If that's cheap, great! What did you say you did for a living again?
I think the "cheapest" way to do the Bahamas might be (these are costs off the top of my head):
1. Nassau
- Stay on Nassau at a place like Orange Hill for ~$90 per person per night
- Dive with Stuart's Cove which costs maybe $100 per person per day for 2 tanks
- Eat at local establishments to keep meal costs down
2. Take a liveaboard cruise like Blackbeard's or the Cat Ppalu which might be $1200-1500 per person all-in for 7 days and nights.
3. Bimini: If memory serves from my recent trip, reviewed in the forum, our hotel and dive package was about $160 pp per day for 2 dives per day, not including meals and not including dolphin snorkel. Plus $70 per day for a golf cart (absolute necessity). Meals were pretty cheap, if monotonous, at local establishments.
I've not stayed elsewhere on land in the Bahamas to know what that would be like. KUFan tells me that there are often cheap deals at mega resorts on Grand Bahama...I can't vouch for the diving though.
Let us know what you find and how it is!