how close is the train station to the bus station is Segovia

They're not miles apart, but the train station is farther from the Segovia center than is the bus station. You may also want to consider how much effort it will take to get to the train or bus station in Madrid for your journey to Segovia to determine the best choice.

We had a bit of a mishap in November 2013, after arriving in Segovia by train the previous evening. Tired, we took a taxi from the train station to our hotel and dinner - no problem there. The next day though, after touring the Alcazar and other parts of town, we wanted to catch the last bus of the afternoon for a visit to La Granja, before heading to Madrid that night. We walked from the aqueduct to the bus station, and there the mishap began. The customer service windows were not open, and although there were several automated ticket machines, there was an issue as to which ones took only cash, and which ones took credit cards. One customer service window opened up for just a moment and we jumped in line to confirm which bus number would be going to La Granja, at what time, and departing from place along the bus platform. No bus arrived at the position along the platform that we understood the La Granja bus would be stationed, although an unmarked, unsigned bus departed from the far end of the platform around the time we had anticipated the La Granja bus. We wound up getting tickets for the next bus to Madrid (after some difficulty with the ticket machine (they wouldn't sell the tickets at the window, directing us only to the machines), and that bus ride was fine, after a confusing loading experience where everyone (not just tourists) waited at the door for one bus, then were directed to another bus, then had to wait for that bus to get a driver to open its door, whereby everyone rushed onboard. There wasn't an organized queue. The buses didn't seem to have a set platform, and there didn't appear to be good signage for departure times, bus numbers, destinations, or loading platform positions, so ask around to make sure you're going to be on the right bus at the right time.

Starting by bus from Madrid sounds like the simpler solution, with departures on the half hour and 1.5-hour travel time to Segovia.

We used the buses in Spain and thought it was very convenient and cheap. Did Avila and Segovia via bus. In the train system was never developed to the level found elsewhere in Europe. Now that the system is slowly being expanded, the ability to location train stations in town centers similar to other parts of Europe is very limited so most of the new station are being location on the edge of the towns. Just not quite as convenient.