Are you aware that a train from Madrid's Chamartin Station will get you to Segovia in about 30 minutes--much, much faster than a bus?
Although I did not use any local buses in Segovia, I have found that European cities usually have a lot more local bus service than we would see in the US. There is likely to be bus service from near the bus drop-off point to the historic center, and there is virtually always a taxi stand outside a train or bus station.
I believe the Avanza bus will make a stop a Calle Jose Zorilla 123, which is about a 1-mile walk from the aqueduct. The train station (which is what I interpret "Estacio" to mean, though I could be wrong about that), is a bit farther from the aqueduct. However, it might be easier to identify the bus stop near the train station (pure speculation on my part).