The Central de Autobuses del Sur is not that close to the airport, and indeed would require a taxi ride that could take hours in traffic. (It's located at the southern end of subway line #2 at Tasqueña.)
There should be buses straight from MEX to Acapulco, so that would be your best bet. Cuernavaca is a pleasant smaller city south of Mexico City, that you'll pass on your way to Acapulco. So taking a bus there, and connecting, would probably work too.