IMO, that's gotten way too complicated for a typical traveler. Most people don't want to deal with a city bus to the airport.
Austin Voters had approved a Multi-Billion expansion of our Light Rail System ( we currently only have one Route, The Red Line Leander to downtown Austin )with a Line from Downtown to the Airport as part of the Plan.
Now Cap Metro has decided to NOT run the Line all the way to the Airport but have the last stop be 3 Miles Short of the Airport on Riverside Dr.
This leaves the Cap Metro Bus that runs every 30 minutes from the University of Texas, thru Downtown to the Airport via RiVerside Drive and Highway 71, as the only Public Transportation to/from the Airport.
This route is mostly used by Airport Employees, but I have found it to be a very conviement way to access the Airport for $1.75 each way.
Still, with the Very Heavy Traffic on all of these Streets, a Light Rail Route is the obvious choice here!