There will be private taxi's at the airport that can take you to San ignacio. Not sure on the exact cost, as it will vary depending on the driver, but I'd guess around $75-100 to get out there. Or you can rent a car at the airport for between $60-$100 per day, price depends on size and quality of the car/truck. It costs about $15 or so in gas to get out to San Ignacio, and takes about an hour and a half.
Also there is a non-stop shuttle service that leaves from the Caye Caulker water taxi terminal at 9:30 and 2:30 everyday. It cost $25 per person to go to Flores, Guatemala, but they stop in San Ignacio too, and would probably charge less if you're not going all the way to Flores.