Last year I took a bus from San Sebastian (Plaza Pio XII) that went to Irun and Biarritz and ended in the bus depot in Bayonne (Place des Basques). I bought the bus ticket at a little office just off the Plaza Pio XII the day before. It was a beautiful ride and the bus was full.
Once you get off in Bayonne, it takes perhaps 15 minutes to walk to the train station to catch the train to SJPP.
The only surprise -- not a problem -- was the ID check after crossing the border. One unfortunate man didn't have his papers. He extracted his bag from the luggage under the bus and went off with the policemen, who were quite pleasant and multi-lingual.
I'm a big fan or Biarritz/Bayonne, maybe because San Sebastian was very hot, even stifling. There wasn't even a breeze along the shore. Maybe it wasn't just the weather. Maybe it was also my Francophilia and my greater ease in French, but I didn't get the charm of San Sebastian. Certainly not in comparison with the French coast.
My biggest regret was not having time to jump off the bus and spend some time in St Jean de Luz.
