Now that I've completed my trip, I'll answer my own question for the benefit of anyone else who might want to know.
Yes, there is a direct bus from Ronda to Sevilla (at least there was as of May 2010; definitely confirm schedule at bus station.)
The bus is operated by Los Amarillos. The direct bus is at 9:30 a.m., 1 p.m. and 6 p.m. every day and takes about 2 hours. There are also several other departures that take you from Ronda to Sevilla but make other stops along the way. The price was 10.86 euros as of May 2010.
Again, definitely confirm the schedule at the bus station. Los Amarillos posted the schedule on their door, but I only got to speak to a live person 30 minutes before my departure when I bought my ticket.
You could get a bus timetable from the TI near the bridge, but that also says to confirm the information with the bus companies.