I walked the Frances in 2012, and was supposed to fly into Biarritz, but I ended up missing my flight and so had to, ah, 'improvise' to get to St Jean! That meant flying to Bilbao, getting a bus to San Sebastian, staying there overnight, getting a bus to Bayonne the next morning, and then a train from there to St Jean, arriving at around lunchtime... about 22 hours later than originally intended!
So, I didn't get the train from Biarritz, although I think the Bayonne train is on the same line. I don''t recall the exact cost, but I think it was reasonable, somewhere in the €10 region. I'm not sure of the timetables, but you might find yourselves waiting for a while if you opt for the train. I looked at that possibility for myself, but decided to make the Bourricot booking. Depending upon how many end up in the mini-bus, it may cost more than the train, but even if it does, it'll get me to St Jean sooner, and that feels like it's worth a few quid to me. That's partly because I feel like I missed out on the St Jean experience in 2012 (I began walking within an hour of arriving on the day), so I want to make the most of my time there this time around!