How can I go from Avila to Toledo without going thru Madrid using public transportation?
You can't.
Norm that was my initial reaction from our experience in that area. But what about the bus?
I suppose it might be possible, by why? You got something against Madrid? If all the reasonable (inexpensive, efficient, convenient) connections go through Madrid, then why fight it?
Yep, even the bus won't connect those two, not even indirectly, unless you go thru Madrid. There some cross-hub connections (eg. Salamanca, Avila, Segovia...or Talavera, Toledo), but nothing connecting North and South except thru Madrid. Too bad, really, since the drive from Avila to Talavera, then into Toledo, is quite nice.