There are GREAT bus connections between Cuernavaca and the south bus station in Mexico City. The best line is Pullman de Morelos. They have a bus station at the corner of Netzahualcóyotl and Abasolo in the historic center, where buses leave every fifteen minutes bound for the Tasquena (south) bus station in Mexico City. The cost of a ticket is about eighty pesos; this gets you a ride on a comfortable, safe, bathroom-equipped bus. You can buy your ticket upon arrival at the station; with departures every fifteen minutes you'll be on a bus in no time!
Getting around Cuernavaca is fairly easy once you figure it out. They have a bus system with their own routes. They refer to these buses as Ruta 18 or Ruta 15. The number specifies the route the bus takes. Each bus can cost a different amount of money, usually never more than 5 pesos. As you see the white buses drive by, in the front left corner it will have a short list (large and bold) of the 4 or 5 major spots it stops at, such as Zocalo or WalMart or Mega. Flagging down one of these buses is simple enough, just stand on the side of the road and wave your index finger or hand for the bus. He will stop for you. If you need off move to the front and tell him or in the rear of the bus there is a small button above the door, just press it. If you can speak spanish and are not sure when you need to get off at a location, just let the driver know, they were very helpful to us when we were traveling around. Try to get a seat if you can, the rules of the road are not the same as in the US. It's not uncommon to have a bus drive into oncoming traffic at breakneck speeds to get around someone. Especially if you're going from Cuernavaca to another small town such as Temixco or Tepatzlan.
Well as all the other bigger cities in Mexico, Cuernavaca as well has several bus stations and they are located at a decent distance from each other. I used 3 of them - 2 for long distance transport (once coming from Mexico City and other time when I went to Acapulco) and one for local. The local one is the most confusing and it represents a typical Latin haotic bus station. There are bunch of buses going and coming all the time and it is tough to figure them out. Luckily, people are great and happy to help confused tourist like I was.
Pullman is one of the bus companies serving Cuernavaca. Luxury buses run directly to the ariport at Benito Juarez in Mexico City in about 2 hours for 100 pesos. This is the easiest way to get to Cuernavaca. There is both smoking and no-smoking sections on the bus. The first bus is at 4:01 AM and that is the one we took when returning to the airport. From personal experience, it is very easy to sleep aboard the bus.
A clear advantage of Cuernavaca is its proximity to Mexico City. Buses leave Cuernavaca to the capital from early morning until 11:30PM every 10-15 minutes from several bus terminals.
I would recommend using Pullman de Morelos. From Mexico City, use the terminal Taxquena located in the South of the city. You can either take a ticket to Cuernavaca "Casino de la Selva" or "Centro". The price is maximum Pesos $90 one/way and the travel time under 90 minutes even with traffic.
There is a "sitio taxi" in the "Casino de la Selva" bus station which offers reasonable fares (e.g. Pesos $50 to the Camino Real Sumiya).
The new bus station in Casino de la Selva is a vast improvement on what was there before - clean, modern, and (so far) much safer. Buses to Mexico City get *very* busy at weekends, and it's always worth buying a ticket in advance, particularly for trips on a Sunday evening.