Traveling between Toledo and Segovia

I know there is not a direct connection between Toledo and Segovia, but wondered what the easiest connection is in Madrid. We can take the train to Atocha, transfer to Chamartin to Segovia - or buses both ways or a combination, depending on connections. I've read a lot of reports, but it seams like the bus stops/stations in Madrid may have changed. Does anyone have current information regarding connections in Madrid? If we can figure out for sure where the bus to Segovia leaves from in Madrid, we could just take a taxi. As it happens, we will be traveling on May 1, which is a holiday, if that changes any recommendations. Thanks,