When I went diving in the big San Pedro Cut a few years ago with Ambergris Divers owner - Roberto Canul, we were surrounded by a pod of about 15 dolphins including babies. It was fantastic. They hung back and watched us from a distance and then they began playing, jumping out of the water and racing around chasing each other.
I have to say I think that was the most memorable dive I ever had - only 1/4 mile off shore from the Sunbreeze hotel. Absolutely remarkable.
When you sail, or even motor out in the blue it is not unusual to see much larger pods, but if you stop and try and swim with them the dolphins take off pretty quickly.
The dolphins have to instigate the encounter, you can't make them come to you unless they want to. Having said that, every time we boat over to Caye Caulker or St. Georges we are typically graced with views of a few dolphins and the occasional manatee.