To travel from San Sebastian to Bilbao we have three possibilities:
Totally unadvised since it takes a long time to cover the route and is very old-fashioned
There is a great motorway linking Bilbao and San Sebastian. You can reac San Sebastian in just under an hour
There is a regular bus service that runs numerous daily routes between the two cities and even goes up to Hendaye in France
Buses Pesa covers the line between San Sebastian and Bilbao airport. The frequency is approximately once an hour. Travel time is 70 minutes.
You can check the timetable here
For San Sebastian, select Donostia-San Sebastian and for Bilbao airport, select Aeropuerto Loiu Aireportua.