The drive from Bilbao to San Sebastián covers 62 miles (99 km) and takes about 1 hr 15 min without stops. That makes it a comfortable one-day drive. Leave in the morning and you'll arrive with the day ahead of you.
About 49% of it is on the AP-8, and most of the rest on the A-8 and the GI-20. You pass Durango and Zarautz on the way.
Expect gentle hills rather than climbs. The high point is around 225 m near Durango.
Expect fuel for a typical petrol car (~40 mpg) to cost around €11 one-way plus roughly €3 in motorway tolls. Prices shift monthly, so treat these as ballpark figures.
At 62 miles this is longer than 8% of the 144 routes covered here, short enough to fold into a bigger itinerary without losing a day.