It's more difficult because you're a single diver.
Reef House Resort on Roatan has single AI rates. $1200 + 16% tax. There's also a good shore dive there. Cocoview with a single supplement will be closer to $1400.
Coconut Tree Divers, Reef Gliders, West End Divers, Native Sons are options with any # of rental properties on the West End. CTD lists some resort options
here. Dives are around 10/$300. Food is cheap. No car needed everything is walking or cabs are cheap.
Deep Blue Resort on Utila - might be more expensive/harder to get to. It's a full AI for $1150/wk. It's 5mins. from town by boat so no car needed there either. Plus you might see Whale Sharks in Sept. Nice place, good food, kind of quiet.
Villablanca Garden Hotel on Cozumel with Dive Paradise - my friend did 15 dives/room there for $800.
Probably Curacao - many apts. rent by the night not PP. There's also escorted shore diving with the Dive Bus but it's not cheap. You'd need/want a car there as cabs are high. Maybe at Atlantis Apts. - Atlantis Diving is on-site. And a shore dive.
Off-water properties on Bonaire. Lagoen Hill is extremely reasonable since it's two miles from the water. You could likely find a buddy at any of the dive resorts, most restaurants, the flight inbound etc. Cars are a little more since ABCarrental has mandatory CDW now.
Maybe a bundled deal with Stuart Coves on Nassau. Hotels on Paradise Island or Cable Beach can be pricey. Look at Orange Hill Inn - they have single pricing. Coves will pick you up for diving but it's 20 mins. to downtown so you may want a car.
At $2000 including flights places you
probably can't afford:
Grand Cayman
Turks & Caicos
I'm guessing Freeport/Grand Bahama also but not sure.
BVI's
probably USVI's also - more expensive than I thought.
Remember it's hurricane season. I'd say chances are minimal in Roatan, Curacao or Bonaire. Roatan hasn't been hit for a while and the ABC's are below the hurricane belt.