I've done that journey twice by bus. It was cheap and comfortable. There is a bus stand outside the Sants railway station.
My flights got into BCN at about 13.30 and the bus left about 15.15. As I recall the journey took about six hours. It cost about €27. I would certainly do it again. One time I wandered into the bus stand and bought my ticket, and the other time, I booked it ahead of time on the internet, printed it out at home and took it to the driver. I really enjoyed the trip which went along at a steady 100KPH on scenic and uncrowded motorways
The company I used is Vibassa and their website is here:
http://www.vibasa.com/index2.php?ididioma=2#
The journey one way is €27.60
One thing though, you will need to prepare in advance the walking route from the bus station in Pamplona to the Jesus Y Maria albergue in Pamplona. The distance is about 1 or 2 km, and you will not have a lot of time before the albergue closes for the night. I did the walk twice, but the first time when I didn't know where it was, I arrived at the albergue pretty late. I don't speak Spanish so I had troubles getting directions. That albergue is a real gem. Best I ever stayed in.
Good luck