The BiciMad program does have an occasional card

http://www.bicimad.com/index.php?s=tarifas

I would recommend taking the bus for a day trip to Segovia. The ave station is quite far from where you want to be as a tourist. Buses leave quite frequently from the Moncloa station.

The train to Toledo should work. If you are reasonable with luggage it should be fine, though not many people will have big bags.