You said, "from the airport in Belize City". Do you mean the Municipal airport in BC, or the International airport which is actually about 10 miles from BC?
Cheapest: taxi to the bus terminal and get a bus. Bus fare to SI is about BZ$7 per passenger. Taxi fare depends on which airport you're travelling from (BZ$6 or $7 from Municipal, and BZ$50 from International).
Easiest: arrange to met at the airport by one of the transfer services (private shuttle) and be driven in a/c comfort. You would have to contact a few services for prices. Some services have prices on their websites.
The BelizeBus website has more details about buses and a list of transfer services...https://belizebus.wordpress.com/