Bilbao airport is 98 kilometres away from San Sebastian downtown.
Many people in San Sebastian uses this airport as the main because it has more flights (international flights go to Bilbao, no to San Sebastian) and is cheaper than hondarribia airport (the nearest).
Te best way to go from Bilbao Airpor to San Sebastian is to book a shuttle in myDrive (Easy and comfortable)
How to get to San Sebastian from Bilbao airport
The easiest and cheapest way to get to Donostia from Bilbao Airport (Loiu) is by bus. There is a direct bus service departing from the airport which will take you to the downtown area in just 75 minutes. (To north train and bus station)
The bus stop is right outside the airport on your right, and the name of the bus company is PESA.
Departures: There is one departure per hour from 07:45 to 23:45.
The bus making the route San Sebastian-Bilbao airport departs on the hour from 05:00 to 21:00.
Price: Single tickets cost 17,10 euros.
More info: Visit this link
Shuttle or Taxi
You can take a taxi near the exit door. May be you have to wait.
Also you can book a shuttle here. This is the best option if you don´t want to wait.
Shuttle Price: About 180€ (4 persons)
Also, you can hire a car if you are goint to use it during your holidays.