Finisterre to Bilbao?

You will have to get back to Santiago. From there you could geta bus to A Coruna and then travel back to Bilbao. Flights from there to Bilbao are around 30 euro.

a few years ago I took a bus to A Coruna, from there to Santander and then to Bilbao, not via Santiago. I stayed over in Santander, my credencial gave me access to the albergue there. It was a really nice trip!
Rolf

Here is the timetable for the buses between Fisterra and A Coruna:
Lunes a Viernes:
Fisterra (Finisterre) - A Coruña: 7:00, 7:50, 9:30, 11:00, 13:45, 16:30, 19:45.
Sábado:
Fisterra (Finisterre) - A Coruña: 10:30, 13:45, 16:00, 19:45.
Domingos y festivos:
Fisterra (Finisterre) - A Coruña: 9:45, 18:00.

And you don't need to book a seat, the buses are never that busy, just turn up at the bus stop outside the albergue in Fisterra.

It is possible to travel all the way from Ferrol to Bilbao with FEVE, though you would need to change trains in Santander and Oviedo. This is also a slow route, as it is a local service which stops frequently.

http://www.feve.es/

From CSJ: FEVE trains http://www.feve.es, not part of RENFE, offer a narrow gauge service all along the north coast of Spain from Ferrol to both Santander and Bilbao. It is a leisurely journey through beautiful scenery and, if you have the time, a trip to be recommended. The journey times are Ferrol-Oviedo 7½ hours. Oviedo to Santander 4½ hours. Santander-Bilbao 2½ hours. It is possible to travel from Ferrol to Santander in one day, provided that the train from Ferrol to Oviedo is not late. Bicycles are carried if space is available.

The timetable is:
dep. Ferrol 0810 arr. Oviedo 1428
dep. Oviedo 1535 arr. Santander 2016

If you prefer a more leisurely approach, the other train of the day from Oviedo leaves at 0905 and arrives Santander 1346, continuing on to Bilbao, arriving at 1646. It is not expensive. Ferrol-Santander 30€. If you are over 60 you can travel half price on FEVE once you have bought a senior citizen’s ‘blue card’ for 2€. All FEVE timetables are at http://www.feve.es.

For an overnight stay in Oviedo there is the Albergue de Peregrinos El Salvador at San Pedro de Mestallón 1, or the Hotel Favila, c/Uria,37, ( 985 259 455 Double rooms 33€, close to the bus and train station. There is a Youth Hostel in Bilbao, Albergue Bilbao (Aterpetxea Bilbo in Basque), Carretera Basurto-Castrexana 70, 48002 Bilbao. A YHA or IYHF card is required.