Not 100% sure but I think you need the T-Zone ticket because the bus you take is an interurban one. The A-Zone ticket is also only valid in the center of madrid according to the map they show on their website.
If you have the chance to ask madridcard via e-mail then do it to check it twice
Hey Simon! Line C-3 is not on the subway service but is linked to it in many stations. Here is the map so you can see it:
http://www.renfe.com/viajeros/cercanias/planos/madrid.html
You should take line C-3 to Pinto and there take a bus numbered 413 which takes you straight to the park.
I hope it gives you some help