Start in Castrojeriz
I couldn't find a train, Alsa bus, Continental Auto Bus or any other bus between Burgos and Castrojeriz.
To find out about local transport you could contact the tourism office in Castrojeriz.
Office of Castrojeriz Tourism
Greater seat, nº3
9110 Castrojeriz, Towns
Tel: + 34 947 377 001
Fax: + 34 947 378 520
Or try the website for Castille-Leon at: http://www.turismocastillayleon.com
There is a 'contact' facility at the end of the page.
Otherwise you could get a taxi from Burgos to Castrojeriz. It's only about 37kms away.
You shouldn't have a problem getting to Burgos from France. All the main Bus services go there:
as well as the national rail - http://www.renfe.es