When I was last in Pamplona (i.e..last September) there was a bus all the way from Pamplona to SJPDP. In fact, several a day. No need to catch a taxi.
I have just checked on the Alsa website and
@ssking14 and
@asaar there are currently four buses a day (Conda, a subsidiary of Alsa) leaving from Pamplona bus station to St Jean Pied de Port - at 10:00, 12:00, 14:30 and 17:30.
It is a seasonable service, but that is what is current i.e. the summer timetable.
If you click on this link, it should take you to the spot where you enter your starting place (Pamplona) and destination (St Jean Pied de Port) and the date you plan to travel, and you will be given a selection of times and prices and you can buy your ticket online...
https://www.alsa.es/en/travel-plans/the-santiago-trail