Can anyone recommend a car service that would pick up at a hotel in San Sebastian and take us to our hotel in Bilbao, in July 2017.
Sorry, I can't help on that, but I assume this could be arranged pretty easily with a regular taxi. I'm sure it's a question your hotel has fielded before, once its guests realize that the train takes the scenic but extremerly slow route.
In case you're not aware, what the locals use is the bus service. The buses are comfortable and take less than 1-1/2 hours.