There are frequent buses from Mexico City International Airport to Puebla. Please note that the place where you should wait for the bus depends on which terminal you are at the airport (there are only two):
* In Terminal 1, the bus terminal is located in the upper floor, near the food court, in front of the vehicular ramp.
* in Terminal 2, the bus terminal is located on Sala D (Hall D), between Puerta 4 (Access door 4) and the gate of national arrivals.
The link to the timetable is
https://www.aicm.com.mx/pasajeros/transporte/autobuses
Please see the first column, the one that indicates "Puebla".
Once in Puebla, please take an official taxi to Hotel Colonial, located at 4 Sur 105 in the Historic Center.
Looking forward to seeing you soon!