The Blue Hole is way out about 60 miles from Belize City. The best way to get there is to fly to San Pedro (20 minute flight) and book with a tour company from that area. There is a Water Taxi that visits San Pedro/ Ambergris Caye/Hol Chan Marine Preserve area but it takes over an hour and fifteen minutes each way. I would love to go out there and scuba dive sometime but I almost think it would be better to save it for a land based trip some time when I don't have to worry about missing the ship.
Here is one tour company that offers a package and the price isn't too bad.
http://grumpyandhappy.com/belize-cruiseships.html