From Mexico city, do I have to go back to the airport to?

take the bus to Queretaro?

Of course not. Depending where you are in Mexico city, you can either go to OBSERVATORIO (M茅xico Poniente) bus station or NORTE.
My recommendation go to M茅xico Norte and take the ETN bus. They are top of the line.

I'm pretty sure you can also go to the Terminal de Autobuses del Norte, the North bus station too, but to be sure, look at the travel guides like Let's Go Mexico and Lonely Planet Mexico, where they'll tell you exactly.