Avanza Bus or Alsa bus?

I don't remember whether I've taken any Avanza buses, but I doubt if it makes a significant difference.

The fare may increase as you get closer to the travel date; I've seen that happen with Spanish bus tickets. I also once had to delay my departure because the bus I wanted to take was already sold out by the time I reached the city where I was transferring. I could have bought the ticket in advance but had not done so.

There are outbound trains at 7:52 and 10:15 AM that cost 11.10 euros each way if you buy a round-trip ticket. Quite a lot of the trains for your date are sold out; others are a lot more expensive. The Segovia trains depart from Chamartin Station and arrive at Segovia-Guiomar.

Does Alsa Bus go from Madrid to Segovia??

In any case, Avanza Bus has lots of departures.

There are, as noted, trains as well. Perhaps depends on whether you're closer
to Moncloa bus station or Chamartin train station.

Of note is that the Segovia train station is a bit outside of town and you need to catch a
shuttle bus or taxi to get to downtown Segovia. Whereas the bus station is very conveniently
located, even though the bus ride is a lot longer than the train ride.

There are one or two bus departures per hour, so I'm guessing they won't sell out.

thank you. i will buy the tickets when we get there.