We took a Autobuses Zinacantepec y Ramales direct bus from Mexico City's Terminal Poniente to Angangueo via Zitacuaro at 120PM. It took about four hours and cost 99pesos.
To leave Angangueo, there are frequent local buses which pass by on the main road (Morelos) and head to Zitacuaro....just flag one down. Since our bags were very large, we waited for a big bus with luggage storage which left around 230PM. There was no central bus station in this tiny town and we just had to ask around to find out information. From Zitacuaro we caught a bus to Morelia, but there are also buses to Mexico City and other destinations.
From Mexico D.F. you first need to go to the Terminal Camionera Poniente near the metro Observatorio.
From there you have two main options: take a frequent bus to Zitacuaro and then catch a connecting service or opt for a less frequent bus that goes directly to Angangueo.
If you choose the latter you are limited to one bus company: Autobuses Zinacantepec y Ramales (tel. 5271 0344). They operate three direct services Mexico D.F. to Angangueo via Zitacuaro at 11:50AM, 1:20PM and 4:20PM. The cost is MXN $90 per person.
Bus lines like Zinacantepec and Alegra offer frequent (every 20 minutes) services to Zitacuaro. They are all 2nd class buses - make sure you get an oxygen mask or a window that can open. That's why I recommend Alegra : rarely on time but most windows can be opened. Cost is around MXN $80 per person (one way).
Once you reach the Zitacuaro bus terminal local buses depart from your left and go all the way to Angangueo via Ocampo. The cost is around MXN $13 per person. The bus will drop you right in front of the hotel Don Bruno (ask the driver).
The travel time to Zitacuaro is around 3 hours. Count one more hour from Zitacuaro to Angangueo.