Hi Auntie Jo. The bus company is Portillo or Alsina Graells, neither of which have a web site and will take quite a while (many hours) to get you there, changing at San Pedro or Malaga.
If you go by train, you have to change at Bobadilla and get another from there to Ronda. Sample times and prices are 09.09 (1.500 Ptas) from Cordoba, gets to Bobadilla at 10.27. Have a coffee and get the 11.45 (1.600 Pts) which gets you to Ronda at 12.31. Unless, of course you manage to catch the 10.32 at Bobadilla - 5 mins to spare - for 605 Ptas, which gets you to Ronda at 11.26.
This information has been supplied by your friendly train spotter (Not!) AF.
Have a good trip! Oh, by the way....have you considered hiring a car. Makes for much easier communications in Andalucia.