hannajo
some thoughts etc
Bilbao is a small airport and if there is no problem with your luggage collection you could be out the main door about half an hour after you land. Then you can either take the bus outside on the right I think to Termibus the main bus station or as we did, take a taxi there. If it is driven by the driver we had last time you should make it in about 20 minutes. More sedate driving might make it half an hour. So it is possible to make that bus.
However unless you are really stuck for time, then why not relax, take the local bus, get off at termbus, get the tram on the street outside and take that along the river and into the old town. I can give you the name of a hotel and a restaurant or two, you could spend the rest of the day seeing the Guggenheim, worth it for the building alone , never mind the art and then the following day, rested, set off for the camino
We have just finished the camino F. in four atapes of about 2 weeks each and one fo the good things about doing it this way is that you get a chance to see other things and towns such as Bilbao, San Sebastian, Vittoria etc. It is not very pilgrim like I know but we like to start and finish our walks with a bit of comfort and culture etc.
Yes there is some thing funny with the ALSA website. It refused my card telling me the bank here at home was denying the transaction but they had no record of such. It appears to be somehting at he spanish end. I got the Camino Travel centre to book the last two seats for us eventually after several attempts and some cursing
If you want more information re Bilbao just ask, we have kept all our bits of paper etc in a scrapbook
Pat