Amtrak also sells a train/bus combination from L.A. Union Station to one of the Palm Springs casinos. The train departs Union Station at 3:10 pm, and connects to the bus at Fullerton. Fare is $19.00 one way. You can take the Flyaway bus from LAX to Union Station for $9.75.
Flixbus also offers service from Downtown L.A. to Palm Springs, but I'm not sure how close their L.A. bus stop is to Union Station.
A one-way car rental is also an option, if the OP has a driver license.