A thread from two years ago:
https://www.caminodesantiago.me/community/threads/bus-pamplona-to-st-jean.65976/
Roughly the ALSA/CONDA schedule over the last few years has been:
Jan No service
Feb No service
Mar 14:30
Apr 14:30 17:30
May 14:30 17:30
Jun 10:00 14:30 17:30
Jul 10:00 12:00 14:30 17:30
Aug 10:00 12:00 14:30 17:30
Sep 10:00 14:30 17:30
Oct 14:30 17:30
Nov No service
Dec No service
The ALSA website in English is at URL
https://www.ALSA.es/en/ and the CONDA schedules are incorporated there. Besides getting the schedule CONDA tickets can be bought online ahead of time from the ALSA website as well.
Note 1: When using the ALSA website to book transportation to St. Jean Pied de Port you must spell out St. in full as Saint or the town will not be found.
Note 2: ALSA does not load its full schedule into the website all at once. I think they publish the schedule only for the next two months. This means that if you try to book a trip through the website for a date later in the year (e.g., trying to book an October 2020 trip in July 2020) the schedule may not be found. This also means that during the winter months the website will make it look as if there is no service at all.
Note 3: ALSA may refuse to accept non-Spanish issued credit cards. In that case the tickets can be paid for using PayPal. Alternatively they could be bought from a reseller.
Note 4: CONDA has a webpage with a schedule. Do not trust this schedule. The last time I checked it had the 2015 schedule. When the webpage is served up it is labelled at the bottom with the date that the webpage was served (not the creation date or date of validity) thus making the information appear to be current. This page is at
http://www.CONDA.es/eventos.php?tipo=3&id=438