There are a few buses as well.. and Ryanair flies twice a day... some times they are cheaper than the bus.. I would get a ticket ahead of time if you want to travel in June, July, or August... otherwise I think you should be ok...
2002 CF: 2004 from Paris: 2006 VF: 2007 CF: 2009 Aragones, Ingles, Finisterre: 2011 X 2 on CF: 2013 'Caracoles': 2014 CF and Ingles 'Caracoles":2015 Logrono-Burgos (Hospitalero San Anton): 2016 La Douay to Aosta/San Gimignano to Rome:
If you plan to return on the Hotel Tren (thereby saving a night's accommodation) I would definitely book ahead. Many people were disappointed - and stuck in Santiago a couple of years ago, when they couldn't get on the train for three days. (That was in mid-June).
I should have added to my posting; if the train is full or you wish to book too far in advance then you will not be able to book on line either. Maybe that is why you are not seeing any way of purchasing tickets.