The bus starts from Plaza de Galicia every 30 minutes, starting at 06:00. Along the way, it stops at the train station, the main bus station, and at several places on the route out to the airport. There is a schedule posted at the Plaza de Galicia and train station stops. The total ride from Plaza de Galicia is about 45 minutes.
Interestingly, the last stop before turning into the airport is immediately in front of Hotel Garcas. This is where I stay when I walk INTO Santiago on the Frances. But, it is an excellent choice to stay near the airport the night before a very early departure.
The one-way fare is (as of May 2017) €3 one-way regardless of where you get on. I have ridden this bus from both the Plaza de Galicia and the train station and it is great.
By comparison, the flat taxi fare from the old city to the airport is €21. If you share a taxi with two or three others, this is not too bad. There are taxi stands at Plaza de Galicia, just beyond the airport bus stop; in front of the train station, and; in the city, at Rua de San Francisco, about 100 meters north of Plaza Obradoiro.
I hope this helps.