Current plan is to go by train from Bilboa to Bayonne on Sept 8th...And to St. Jean on Sept 9th

Euskotren (Bilbao to Hendaia) does not require a reservation ... its a commuter train.

SNCF TGV and Intercites trains (Irun to Bayonne) require reservations (which can be obtained at the train station). You cannot reserve a seat on SNCF TER (TER 61 Hendaye to Bayonne, TER 62 Bayonne to SJPdP) trains.

Did you know PESA operates buses on a frequent schedule from Bilbao (Loiu) Airport to Donostia/San Sebastian bus station? Then catch the Euskotren at San Sebastian Amara to Hendaia. You might make Bayonne in time to catch the last train to SJPdP.