Hi Prilia,
Second part first, there are many buses from Burgos to Santander, their schedules are on the website. It is a very pleasant trip through nice countyside and mountains.
Accommodation is plentiful within walking distance of the bus terminal at Santander, we booked to stay at a E30/night ensuite hotel, but as it was not available at the last moment we then had alternative similar accommodation arranged by the first hotel at the next street.
It was done very efficiently, little English was spoken though.
Buses run regularly from the bus terminal to the distant airport, I am not sure of the time of the first bus but you can arrange the airport transport by asking the hotel. The check-in at Santander, and the boarding of the aircraft can be chaotic so please be early. The immigration can be a bottleneck so if you do not hold a European passport make sure you get the proper forms to fill in before you join the queue, otherwise you will have to go back to the end of the queue to fill in the form and start again.
Joe