We'll be arriving at noon at Madrid Barajas (from FRA) and would like to catch a 2:00PM AVE at Atocha Station. Is that enough time using bus and Cercanicas trains?
I doubt you'll have enough time by the time you go through immigration. A better way to get there may be the Metro, there are about 3 transfers but they are quick.
The only way you'll have any chance of making that connection is to take a cab....about 30 Euro from Barajas to Atocha. Might be less stressful to take a later train...or, if you're heading for Barcelona, to see if there are any cheap airfares left for your travel date on Spanair or Vueling. That way, you don't have to leave the airport.