By car: The distance between Bilbao and San Sebastian is about 100 km, the two cities are conntected by the (toll) highway A-8. Alternatively, you can take the country road along the coast, which also allows you to access all the touristic resorts. If you need to rent a car, it will be much more economical to reserve it before your travel than if you rent it when you arrive to the airport. Here you find some great rates for car rentals.
From the port of Santurce (in basque: Santurtzi) there are ferries connecting Bilbao with the British Portsmouth.