It's an express bus and the airport isn't a scheduled stop, so I don't think it will stop to let you out at the airport. But, if you keep your luggage with you in the seating area, you could try and ask the driver if you can get out. It's not unusual for the express buses to stop along a route.
If you don't mind night buses, there are a couple of express buses that depart from Chetumal (at 10 pm and 12:30 am) and go direct to the airport
Are you certain of that? I asked at the Water Jets office today and they were adamant that no buses went to the airport from Chetumal, that you had to change buses in Playa or Cancun.
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