Taking the bus from Bilbao Airport to San Sebastian is a good way to get between the two cities in the Basque Country when you are visiting Spain.
There is a regular bus service that runs from the airport to San Sebastian. A company called Transporte Pesa runs the service. Their buses depart every hour throughout the day, so you can travel whenever your flight lands. The first departure is at 7:45 (6:45 on weekends and public holidays) and the last is at 23:45.
Bilbao Airport buses depart from outside of the arrivals halls and arrive at the bus station in San Sebastian. The service is direct unless passengers alight at Zarautz en route.
The journey time from the airport to the city is 1 hour and 20 minutes if there is no traffic.
Tickets for buses from Bilbao Airport to San Sebastian cost 16.50 euros each way. You can purchase them when you arrive at the airport.