That's a beautiful rail line, I did Gijon to Bilbao on it, wonderful.
I've used trains with a bike all over Spain and without a problem, metro, local short/medium distance. But I've never used the Talgo train (fast long distance) and I think that is where bike problems lie. The trains are very cycle friendly, some lines have lower floors in the cycle carriage and an automatic step than lowers on arrival to that you can just wheel in and out, nice.
Agree with Andy, no point in camping in Spain unless you really want to, rooms are very cheap, especially above bars where they may not be visibly advertised, ask.