Bilbao Airport local bus to Bilbao Termibus. Termibus is co-located with San Mames station. PESA bus Termibus to Place de Basques Bayonne or Euskotren San Mames to Hendaye France. SNCF train Hendaye to Gare Bayonne or ATCRB bus to Place de Basques Bayonne. Chronoplus bus from Place de Basques to Gare Bayonne. SNCF train Bayonne to SJPdP.
PESA bus option is probably easiest but runs only twice daily.
SNCF train from Hendaye is preferable to ATCRB bus but runs less frequently.