Bus from Santander to Sahagun September 2015

Renfe train from Santander to Palencia and Palencia to Sahagun. The results are somewhat confusing if you ask the site for information Santander to Sahagun.
http://www.renfe.com/EN/viajeros/

ALSA bus from Santander to either Leon or Osorno and Leon or Osorno to Sahagun. The ALSA site will not give information Santander to Sahagun.
https://www.alsa.es/en/

The train runs more frequently than the bus.

From (downtown) Santander to Sahagún, train is your best bet (IMHO). You are traveling on a Sunday and there aren't buses from Osorno to Sahagún on Sundays (AFAIK). To go by bus changing buses in León would be possible but it would be a bigger detour than to go by train changing trains in Palencia.

To look for trains from Santander to Sahagún on the web of RENFE, make two separate searches: one for the route from Santander to Palencia and another one for the route from Palencia to Sahagún and decide by yourself what's the best connection for you. The web of RENFE isn't (very) good looking for options involving a change of trains so if you just look for options from Santander to Sahagún, you are unlikely to see them all.

From the airport to downtown Santander, take an Alsa bus (they run frequently). The train station in Santander is in front of the bus station.