It usually takes at least 1 hour and perhaps up to 1.5 hours to get through the airport and get to Belize City.
There are later water taxis...
Caye Caulker to San Pedro at
> 4:30 (Caye Caulker Water Taxi)
> 5:30 (San Pedro - Belize Express)
> 6:00 (San Pedro Water Jets Express)
Let me know if you need the links to the websites of the water taxi companies. The sites have complete schedules & fares.