CONDA buses run from Pamplona to SJPdP 7 days a week. Usually the last one leaves by 1800. Last summer it was 1730. See ALSA schedule when it is updated in mid April.
CONDA is Navarra's bus line but it was bought out and the ALSA bus line is one of the owners. CONDA schedules can be brought up on the ALSA website and tickets can be bought online through it. Further below I describe how to find the current Pamplona-SJPdP schedule. ALSA may not show service for dates too far in the future.
I do see a year-round schedule at
http://www.conda.es/eventos.php?tipo=3&id=438 (in Spanish) but I'm not sure how up-to-date this page is (although it does give a copyright date of "Lunes 23 de Enero de 2017" at the bottom of the page I think it really refers to when the page gets served rather than when the content data was updated.)
The page shows that from March 1 through November 2 there is a bus departure from Pamplona to Saint Jean de Pied de Port listed at 14:30 and from April 1 through November 2 there is another departure at 17:30. Later in the year there are departures at 10:00 and 12:00.
* 10:00 (1/6 - 30/9) (1 June - 30 September)
* 12:00 (20/6 - 5/9) (20 June - 5 September)
* 14:30 (1/3 - 2/11) (1 March - 2 November)
* 17:30 (1/4 - 2/11) (1 April - 2 November)
Note that this schedule does not show any service between 3 November through the end of February.
To get the current Pamplona-SJPdP schedule go to https:/
www.alsa.es/en/ and click in the "Point of departure" type-in box. A pop-up allows you to pick a "Departure country" of "Spain." Then in the "Point of departure" box start typing "Pamplona" (without the quotes). As you type the name the pop-up starts showing fewer and fewer names until you can either finish typing or click on one of the names shown in the pop-up. Next do something similar in the "Destination" type-in box and pick "France" in the pop-up. Go back to the "Destination" type-in box and (this is the secret) type in the name "Saint Jean de Pied de Port" (without the quotes). If you abbreviate "Saint" as "St" or "St." then Alsa won't find the town.
A caution when viewing Spanish schedules and calendars. The week runs from Monday to Sunday; not Sunday to Saturday. This bit me once but since the easiest fix was to book an extra night in Barcelona I didn't mind.