Astrogirl,
That's exactly what I just did, and I don't consider it an error at all. Bilbao is the best place to adjust from jet lag, there's the Santiago cathedral where you can get your first sello, and of course, the Guggenheim Museum. It's also where I left my luggage before setting off for SJPP; wonderful staff at the Hotel Bilbao Jardines at the Casco Viejo.
That's right, you take the bus to Hendaye, then take the train to Bayonne and onwards to SJPP. In the Hendaye station you can buy the tickets for the 2 train journeys. A train journey is always better than a bus; you can take a walk along the aisles any time and there's the toilet available.
A couple of German ladies I met in the Bilbao Termibus took the same bus but went all the way to Biarritz; I left them in Hendaye. I was told later they had to transfer to another bus or take a taxi to Bayonne. I arrived in Bayonne much earlier than them. And they were almost late for the SJPP train.
From Santiago de Compostela back to Bilbao there's an overnight bus that leaves at 6 PM and arrives in Bilbao at 5:30 AM, although I strongly suggest you take the train.
Mark