Anglet airport serves both Biarritz and Bayonne.
For ease of getting to Saint Jean Pied de Port it would be best to spend the night in Bayonne and travel to SJPdP the next morning.
In Bayonne the simple
Hotel Monte Carlo is good inexpensive choice located opposite the rr station. Nice cafe and resto also. Here is
their web .
From Biarritz airport (Anglet) take a Chronopost bus 14 to the BAYONNE rr station (Gare SNCF).
Travel time is roughly 30 minutes.
At Bayonne station take a regional TER line 62 train to SJPdP.
Generally there are several TER line 62 trains from Bayonne to SJPdP each day.
For current schedule see
https://www.ter.sncf.com/aquitaine
Bon voyage and Buen camino!