I use the ticketbus site to find schedules & fares, but I've never tried using it to book a ticket:https://www.ticketbus.com.mx
There is also an ADO website, but I prefer ticketbus.
Some travel agents on the mainland (in Belize) sell tickets for the ADO buses. I don't know about Ambergris, but ask around and you should find one.
The ADO express buses to Cancun City depart about every 2 hours from the ADO bus terminal in Chetumal. I haven't yet been on a bus that has been full, so you should be able to buy a ticket as soon as you get to the bus terminal, and get the next bus out.
The trip will take about 5.5 hours and terminate at the Cancun bus terminal. You then have to get a bus or taxi back south to the airport.
Perhaps some travellers get off in Playa in order to get one of the airport shuttle buses, thus avoid the bus trip to Cancun then backtracking to the airport; that should be about 20 to 30 minutes.
There is only one express bus that goes from Chetumal direct to the airport -- it departs at 30 minutes past midnight. You should be able to find it on ticketbus.
The ADO express buses are excellent -- a/c, reclining seats, video, toilet. Take something warm to wear because the a/c is usually set to "Freeze".