Leave Estella 1045
Arrive Irun - Front Hendaya - Parada en Puente de Santiago
(Which is 'stop at the Santiago Bridge')
From whence you cross the Santiago Bridge from Irun to Hendaye on foot.
After crossing the bridge, turn left and walk towards the railway tracks then turn right and continue till you reach Gare d'Hendaye.
Or
Leave Estella 1045 and arrive at Irun Renfe Station at 1300, exit the Renfe station, turn right then walk across the bridge over the tracks to Station Colon on the left (North) side of the street.
Take Euskotren from Station Colon to Station Hendaia which is co-located with Gare d'Hendaye.
From Gare d'Hendaye
a. Take Transports64 bus #816 to either Biarritz Airport or Biarritz La Negresse leave 1323 arrive La Negresse 1433 (vicinity of Gare de Biarritz). Walk 1 block to Gare Biarritz and take Chronoplus bus A1 to downtown Biarritz.
http://www.transports64.fr/IMG/pdf/cg64-tiu64-fh105x150-816-new-2015web.pdf
b. Take SNCF train to Gare de Biarritz and then Chronoplus bus C to either Biarritz airport or A1 to Biarritz City.
SNCF
http://www.sncf.com/en/passengers
Chronoplus
http://www.chronoplus.eu/
Your other option is to get off the Estellesa bus in San Sebastian. ALSA and PESA offer bus service from San Sebastian to Biarritz. PESA stops at Gare d'Hendaye and ALSA stops at Irun Renfe Station.