Shuttle to Ronncenvalles for Mass

The short answer is 'no'.

Transportation options between Pamplona and SJPdP:

-Autocares Artieda is regional bus service from Pamplona to Roncesvalles. It does not operate Sundays. Usually twice daily.

-CONDA (ALSA) bus travels from Pamplona to SJPdP. You cannot use this service between to travel between any two points from Pamplona to Roncesvalles as the rights belong to Autocares Artieda.

-Express Bourricot is Private Hire taxi and luggage service that caters to Pilgrims and is based in SJPdP. You'd have to contact them to find if they will operate passenger service past Roncesvalles.

-Taxi from SJPdP or Pamplona. There might be local taxi service at the villages but you'd have to inquire there to find it out.

Burguete is roughly 3 km after Roncesvalles. It is an easy walk.
This Gronze.com list includes accommodation possibilities in Burguete. You might email one or more with your request.

https://www.gronze.com/etapa/roncesvalles/zubiri

Good luck and Buen camino!

Staying off the main stages between Roncesvalles and Pamplona isn't easy, at least not if you want/prefer to stay in albergues ;-) If you stay in pensions/hotels ect. you will anyway need to reserve them and at that point you could ask if somebody from the hotel can you drive up for the mass to Roncesvalles.

Buen Camino, SY