Even for those going to Mérida, one can sometimes get such good fares into Cancún it pays to do that, take the bus or shuttle to the Terminal Camionera and take the ADO bus to Mérida - economical, air conditioned, pretty plush seats and
much more comfortable than the airplane you came in on.
There are usually two direct busses to Mérida from the airport. The rest of the time, you will take their shuttle to the downtown bus terminal. ADO shuttles are at both airport terminals, and you can usually spot a kiosk where you can buy tickets; your bags will be put in the belly of the bus, and you will arrive at the downtown terminal to catch your bus to Mérida (or elsewhere). If a taxi driver or a shill tells you they do not exist, beware an impending ripoff attempt. A porter can schlep your bags and take you to the right place - just say "ah, day, oh?" Tip a buck a bag or so and he will be very happy.
When you arrive at the downtown terminal, take your baggage to the ticket counters, if you do not have your tickets yet purchase them and check your baggage - just as you did at your departure airport - and they will give you baggage checks to present at the other end of the line. Seats are assigned when you purchase your ticket; there is no GuruDeAsientos to guide you, but they do have a chart they can show you at the counters.
ADO (ah-day-oh, Autobuses del Oriente) has three levels of service - ADO, ADO-GL and ADO Platino. ADO is First Class (really), GL is luxury and Platino has fully reclining seats with eye masks, blankets, pillows, etc. and an attendant who can get you snacks or soft drinks. The Platino service also has a VIP lounge to wait in.
Cancún to Mérida on one of these fast busses is about four hours. The price is currently between USD $22.50 and $40, depending on class of service, Nope, no pints I am aware of!
Airport to Mérida busses take about four hours and are the ADO (First) busses; departures currently at 1:30, 3:30 and 5:00 PM only, a premium price at USD $35-37.50 (500 MXN) but comfy and fast. Most end at the downtown bus terminal and many stop at Altabrisa and the Fiesta Americana (all "local" CUN - Mérida busses currently do so).
You can see schedules and pricing
here on the ADO website, but it's only in Castilian spanish.
No, I would never hesitate to take a first class or luxury Mexican bus. The drivers are very professional, there is GPS speed monitoring, they are far better than any bus I have ever seen in the USA and I have taken ADO, Estrella de Oro, Cristobal Colón, Estrella Blanca and Autobuses Pullman de Morelos - eben one or two overnight busses in Mexico (reclining seats, etc. with bathroom, and maybe a little swaying). The very local intertown "chicken" Flecha Roja, etc. busses, well... I've taken them, too, but would not recommend that for you!