I'm also interested to know the answer. I think I know but am not sure if it is correct. Thanks.
I traveled to Segovia from Madrid last month, and bought a ticket from Le Sepulvedana in advance. I was surprised to find when I arrived to the station that the bus actually leaves from Moncloa (accessible by the tren circular). You may buy your tickets online or in Moncloa. Then head up the escalator to the platform 8/9 level 1. THe platform names are very confusing so make sure the screen says Segovia. People in the station are very helpful.
Thank you so much for all the help and advice!
We visited Segovia from Madrid by La Sepulvidana bus. We didn't book a train ticket in advance as we were not sure if we would be able to fit it in our itnerary. Madrid itself has lots to see and we had 3days only. So glad that we could make it on the afternoon of the third day. We reached Moncloa by metro from Atocha and the bus station Intercambiador was a floor above as far as I remember. People at the station n shops are very helpful and guide well enough. Buses leave every one hour or so. So we took the bus at 2:30 afternoon. At the Segovia estacion, there is a tourist office and the lady was extremely helpful and advised us to buy the return ticket and then go sight-seeing. So we bought the return tickets for the bus at 9pm. It was all very smooth.
Segovia is a place not to be missed. We didnot do the cathedral but the Aquaduct and Alcazar are truly awesome. Took the tower tickets in the Alcazar to get views of Segovia but I felt we could have given that a miss as it was a good climb! Also had the special suckling pig/lamb and the lipsmacking segovian punch at Meson de Candida.