Busing in Mexico can be everything from a "chicken-bus" adventure stopping at every hill, dale and tope for passengers and their goats, chickens etc. to a very luxurious experience in modern European-built busses with reclining seats, air conditioning, stewardesses to serve you snacks and cold beverages, W.C.s etc. driven by professionals watched over by GPS satellite reporting devices. In any case, it is economical. Nothing like them in the US at all, never has been.

A somewhat klugey site but one that can give you a good idea about the levels of bus transport, seating, origins and destinations, prices, etc. is

https://www.ticketbus.com.mx/ticketbus/inicio.jsp - the site is available in (Castilian) Spanish, and more or less in English, French and German. It can be a little user-unfriendly on occasion, but it has lots of information. Be aware -larger cities have several bus terminals, often with several lines departing for a particular compass point or series of destinations, or even specific bus lines. "Mexico" means Mexico City, which has several terminals, including at the international airport (departures for Cuernavaca and Puebla iirc, but "Mexico Aeropuerto - Puebla" will reveal - nothing! because Ticketbus does not sell these and they are available to walkup passengers form the airport booths.)

Theoretically, you can even buy your bus tickets via this site; I have never tried it, but have used the excellent Premier and similar deluxe level bus service between cities. (Advance purchase, even if one day, is important in any case - seats are reserved on these higher-level busses.)

Cancún - Palenque luxury service is provided, according to Ticketbus, by OCC (3 busses, Omnibús Cristobal Colón,) ADO (Autobuses del Oriente) and ADO GL (ADO Gran Lujo - the luxury express.) These are all overnight services with more or less reclining seats (best is GL) taking about 12 hours and costing under USD$50 to $55 one way. Depending on how you see it, you can get there and save a hotel night. These are all reliable, safe busses.

Alternatively, take a LCC like Click! Mexicana from CUN to VSA (Villahermosa, Tabasco, a huge PITA because you probably will have to transit via MEX!) or VW - Aeromar direct CUN-VSA, ATR about two hours, one stop in MID. Take a bus to Palenque from there - two hours, several every day.

The you have to get out to the ruins of course...I'd spend a couple of days in Palenque, at the Hotel Chan-Kah if I could afford it - it is away from town, nearer the ruins, you can catch the van there, and you can see all kinds of wildlife at this lovely place - and take a nice dip in the pool when you want to cool off. (There is also a Chan-Kah Centro in the center of town, not what I am talking about.) At the very, very least, download the Palenque maps from their site. (You can reliably book online here; keep the information and name of the person you deal with.)

We stayed here with some Aussie friends we were introducing to Mexico last year, and they loved it...