Buses on Sunday

Yes, buses run from Pamplona to SJPP on Sundays, but it depends on what month you need it.

From now through 31 August, there is a daily bus at 0800 hours, Sundays included.

From now through 30 September, there is a daily bus at 1400 and 1730 hours, Sundays included.

If you need it for after these dates, do a search for your exact date here: https://www.alsa.es/en/buy-and-schedules/international/?searchType=international

Note that there is no bus from Pamplona to Roncesvalles on Sundays, and the SJPP bus does not stop there.