Vehicle transfers Bilbao, Biarritz, St Jean etc.

Offer of transport between Biarritz and St Jean - Roncesvalles - Pamplona.

We offer to all the pilgrims who will start the road from Saint Jean or Roncesvalles a very economic price in transfers from Pamplona

I'm not sure about taxi prices in Madrid but you could get the train from the airport to Atocha Train station.
In September there is a bus from Pamplona to St Jean in the afternoon. Also, you could contact Taxi Fermin to share a taxi.

Pilgrim Taxi or Taxi Peregrino is a special service that Teletaxi San Fermín provides for anyone starting the Camino de Santiago in Navarre and needing transport from Pamplona (the bus station, the railway station, the airport or any other starting point) to Roncesvalles or to St Jean Pied de Port.
All you have to do is fill in the form to make a booking for the day and the time slot required, from the starting point you specify. Filling in the form is quick and simple, and won’t take more than five minutes. We hope to give you complete satisfaction with our service.

http://www.taxipamplona.com/comparte_en.php