Zubiri start

The bus from Pamplona will probably be Autobuses Artieda; see
http://www.autobusesdenavarra.com/siv/internet/itinerarios.jsp?codigoEmpresa=110&codigoItinerario=80
There are two private albergues in Zubiri, that is, Zaldiko (the oldest and more popular), and Palo de Avellano (new, more comfy, apparently); and the municipal one.
Pamplona is a pleasant, interesting city.
Buen camino!

Since you plan to bus from Madrid to Pamplona why not start walking west on the camino directly from Pamplona ? Whatever you decide do take care descending the Alto de Perdon; it's a doozy and especially difficult in fog or heavy rain!!

MM

If you start in Zubiri, take note that the Camino goes on the other side of the old bridge. There is no evident signpost in Zubiri proper. I took the wrong way, and walked some uninteresting miles by the highway, until I managed to retake the right road.
As a fellow pilgrim told me, "well, now you have a good excuse to come back another year..."

I'd recommend double checking the bus times when you get to Pamplona.

In September there are two buses a day (M-F) from Pamplona that stop in Zubiri. The first is at 1:00pm and it's a small bus used mostly by the locals. The second bus is the large coach at 6:00pm that is full of pilgrims going to Roncesvalles. On Saturdays the large coach departs at 4:00pm instead of 6:00pm. There is no bus, big or small, on Sundays.

The fare from Pamplona to Zubiri is 2.10 euros.

Here is the info on the 1:00pm bus:
http://www.autobusesdenavarra.com/siv/internet/itinerarios.jsp?codigoEmpresa=110&codigoItinerario=96

Regarding the albergues in Zubiri, you can book Albergue El Palo de Avellano via email or phone. In my opinion (after staying in Zubiri at both private albergues and several pensions), El Palo has the nicest facility (15 euros for bed and breakfast) and the best dinner (12 euros) in town. According to the listing on the Eroski site, you can book Albergue Zaldiko only by phone, but email will likely work, too.

El Palo de Avellano: http://caminodesantiago.consumer.es/albergue-el-palo-de-avellano
Zaldiko: http://caminodesantiago.consumer.es/albergue-zaldiko

Regarding time in Pamplona, I think it does warrant some time to look around. Food, architecture, gardens, history, the bull-run route - all interesting! - and Pamplona has all the services you may need such as the post office, cell phone stores, gear shops, and supermarkets. The only reason you might not want to spend time in Pamplona is to keep pace with your new pilgrim friends who are walking farther than Cizur Menor the next day. In any event, since Cizur is only 5 kms from Pamplona, you should have no trouble finding a bed if you arrive mid-afternoon.

Buen Camino!