To travel from Madrid to Lourdes via bus...
1. Go to WWW.ALSA.ES
2. Go to the international route
3. Choose your route: Madrid ( Plaza Elíptica) ---> Tarbes
4. Book a pickup from Tarbes Train Station.
We used the taxi service of ALLIANCE: firstname.lastname@example.org
Note There are some trips that arrive 2 or 3 am. The earliest train from Tarbes to Lourdes is 6 am.
This is a cheap route but it takes a lot of time. The bus ride takes 13-14 hours with a 1 hr stopover in SOCU. This is also where you change buses.
Personally, I didn't mind the long travel time. It was a pleasant and comfortable journey. Expect magnificent views as the Spanish Country-side looks like a beautiful painting. It was like starting into a screensaver.
Be sure to bring food and drinks. The chips and cookies in SOCU are way overpriced. Try to save some videos on your Android or bring a book too. NO WIFI IN THE BUS.