Hi Niel,
It looks as though the bus arrives at Avenida de America at 9h55 and departs at 10h15 to collect from MADRID Est SUR - at 10h30. (PIEDRAFITA 09h55 - 16:25 28,95)
Here is a link to the metro:
http://www.metromadrid.es/ Click on Plano de Metro to download a really good metro map.
To get to the Bus Station from the airport, go down, down, down the escalators till you are in the metro station.
It can be scary trying to buy a ticket from a dispensing machine when you can't read Spanish, and might not have the correct change, but there are always guys in uniform close to the machines. Just ask one "Avenida de America por favor" and I'm sure they will help you!
The airport line is No 8 - the PINK line. Get off at Nuevos Ministerios which is a huge interchange station and follow the signs for the Avenida de America station.
The metro station at Av. de Americas is a big one, 5 or 6 floors if I remember correctly. They have escalators (which work most of the time!) but you will have to find your way down to the area where the buses leave from.
You could also take a bus to Ave. d. America but it might be quicker by metro.
Buen suerte peregrino!