I travelled by bus Santander-Barcelona last July. I con't remember the Bus Company's name (I got it from
el Diario de la Montaña). But when I went to the Bus Station to buy my ticket I found out it was operated by Alsa. It listed a stop in Bilbao; but it didn't.
Maybe it is like a 'flag' stop where it only stops if there are ticketed pax waiting.
Just go to Bilbao's main bus station and find out which busline serves that route. The one from Santander-Barcelona has a day run at about 09:00 and an overnighter at about 22:00. The Bilbao schedule is probably similar.