You have a couple of options to get from Bilbao to St Jean.
Bilbao to St Jean via Bayonne:
There are only two buses a day from Bilbao to Bayonne - at 7h30 and at 1300 hours - it takes 3 hours to Bayonne. The company is PESA -www.pesa.net
If you take the 13h00 bus you'll get to Bayonne at 16h00.
The next bus to St Jean leaves at 18h12 and arrives at 19h35
Bilbao to St Jean via Pamplona:
There are 6 buses a day from Bilbao to Pamplona. 10h00 13h00 15h30 18h00 20h30
The bus takes 2 hours and costs 13,40€
The bus company is
http://www.laburundesa.com/
If you get the 13h00 bus you'll be in Pamplona at 15h00.
From Pamplona you can get a mini-bus taxi to St Jean with Express Burricot.
http://www.expressbourricot.com/
email Caroline at
apcaroline@hotmail.com to arrange for her to pick you up at the bus station. She usually collects pilgrims from the bus station at around 16h00. The charge depends on how many other pilgrims are in the taxi.
St Jean Pied de Port
I recommend that you book a bed at the Esprit du Chemin albergue for that night.
info@espritduchemin.org
And, also reserve a bed at Orisson if you intend breaking your first day here:
jean-jacques.etchandy@wanadoo.fr