greyhound doesn't go from LAX. You have to go to downtown LA to catch the bus. There is no public transportation from PSP airport to Indio...well unless you want to take the 10 transfer 6 hour ride on the Sunbus system.
Oh and those of you who take greyhound from LA, whatever you do DO NOT GET OFF IN PALM SPRINGS. You need to get off in Indio, otherwise you'll be $70+ short for a cab ride to get to Indio.