Whizzer,
I leave this week, US to Madrid. I'm taking an Alsa bus to Pamplona, which leaves directly from Terminal 4 of the airport. (purchased ticket online) While I prefer to travel by train, I didn't think there was enough time to get a cab to the train station (across the city), to catch the express train. In Pamplona, I will be met by Express Bourricot for the transfer to SJPP. You can check all train schedules by googling Renfe, and bus schedules by googling ALSA bus.
The only important advice I have from experience: I live near SDC in the Summers. In the last 10 years or so, I have had about 20-30 different groups of American friends visit, connecting through Madrid. Honestly, I am not sure a single group has EVER arrived without missing at least one piece of luggage. The lost luggage always appears, but generally a day or two, and many frustrating phone calls later. It seems trans-atlantic flights have a habit of getting a bit delayed, and the luggage just doesn't seem to make it to the connection in time. While I am sure many people have positive experiences with this, I personally, would consider checking my Camino bag though Madrid to a second destination, just too risky.