Peter, we drive from Santander to Biarritz each year. The road from Bilbao to Biarritz is a combination of motorway and dual carriageway. The only difference is that they charge on the motorway section, the type of road is the same. There are also some major road improvements going on on some stretches (for the last couple of years) so expect some speed restrictions and contra-flows.
The road is steep in parts, with spectacular scenery, but as you can usually get a decent run at the inclines you shouldn't have a problem and certainly shouldn't have to do any hill starts, especially in reverse. You'll be fine.
Before the motorway was completed it was a slow winding route through quite a lot of small towns and villages.You don't want to consider that option.