I would love to stay at Turneffe, but it is VERY expensive, especially for a single traveler.
There are shops from AC that go to Turneffe on occasion. It would be an all day excursion with two or three dives and lunch included. The shop will likely need a minimum number of divers because of the distance and fuel costs. So there are no guarantees of going to Turneffe if you are on AC. You are very likely to find boats going to the Blue Hole at least once a week as long as the weather is good. If the shop you are diving with is not going to Turneffe, the shop will often be willing to call around for you to see who is going and book you. I still haven't done Turneffe but hope to during a future trip.
In terms of budget, that's a great benefit of AC. Lots of choices for lots of budgets.