Zaragoza to Burgos

http://www.aena.es/es/aeropuerto-zaragoza/transporte-publico.html

Spanish airports seem to be adopting the same website design which includes on the home page 6 huge buttons, one of which is for public transport to and from the airport. That's the link above.

Once you are on the piblic transport page you find a link to the Alsa website where you can find which ever bus you need.

https://www.alsa.es/

So, in this case, the airport website tells you that for 1.85€ you take the bus to anyone ofmthese stops in Zaragoza: Línea que une el aeropuerto con el Pº Mª Agustín, 7 de Zaragoza, y paradas en PLAZA, plaza Imperial y la Estación Intermodal.

Get off at the Estacion intermodal, and voilà!

As per the Aena Zaragoza website, take the local bus which runs every 30 minutes. Go from the airport to a large building marked Adif Zaragoza Delicias.

http://www.adif.es/es_ES/infraestructuras/estaciones/4040/informacion_000020.shtml

Autobuses Jiminez provides service from Zaragosa Intermodal Delicias to Burgos.
http://www.autobusesjimenez.com/