Dan listed the website for the bus lines in Mexico. If you know the arrival time of your flight in Cancun, you should have no problem booking the bus. You can even buy your bus ticket in advance online now. So should have that information ahead of time to book your taxi. If you give Henry the time the bus leaves, and from where, they keep tabs on them via radio to see when they are arriving.
The Mexican taxi drivers got up in arms a year or so ago, which is why the Belize taxis can no longer pick up passengers at the Chetumal bus station. You must take a local taxi to Los Cocos or another specified location within Chetumal and they will pick you up there.