from Patzcuaro to Guanajuato

Fastest would be a taxi...Best,I think, would be bus, changing in Morelia & Celaya...carracar

THere are two daily, non-stop departures on Primera Pus from Pátzcuaro to Morelia. (Other lines have more frequent runs.)
11:20 and 11:50, arrives Morelia Camionera de Autobuses at 12:45 and 13:15, respectively.

There is one daily Primera Plus departure from Morelia to Guanajuato.
Morelia/Guanajuato - 28/02/2007 Adulto : $143.00

No. Servicio 160

Hora Salida 15:15

Hora llegada 18:50

Escalas (stops): 2

From http://www.flecha-amarilla.com.mx/</a><BR><BR>

Since the OP did not mention buses, perhaps he means by driving. The way I drive from Patzcuaro to Guanajuato is almost traffic free and involves zero "nervous driving". It is fast only if you know the route well, as it can be confusing to the uninitiated, even though it looks easy on a map. I go by way of MX Routes 15, 37, and 84. That is by way of Quiroga, Zacapu, and La Piedad, in Michoacan, and Romita, and Silao in the state of Guanajuato. The confusing part is between La Piedad and Silao. Even faster is to avoid the La Piedad to Silao section, and go from La Piedad to Irapuato, but expect heavy traffic, crazy driving, and getting lost in Irapuato. (for the uninitiated)

However, the average person would probably prefer driving by way of Morelia, Moroleon, and Salamanca. Even this one can get you lost, in the Salamanca area, if you are not familiar.