Here's LAWA's website for the FlyAway and here's some more information from their press release:
Los Angeles World Airports, in partnership with Metro (L.A. County Metropolitan Transportation Authority), is launching a new non-stop FlyAway bus service from Union Station/Patsaouras Transit Plaza to LAX airline terminals. The service starts this Wednesday, March 15. The 20-mile ride costs $3 one-way for adults with discounts for children,
and takes no more than 45 minutes during rush hour traffic because it uses freeway HOV lanes. This is one of the most significant ground transportation initiatives LAWA has conducted in many years. In addition to providing inexpensive, convenient (every 30 minutes, 24/7 including weekends and holidays) service between LAX and Union Station, the service will help reduce traffic congestion, eliminate thousands of commuter miles annually, and contribute towards cleaner air. We believe this service will become just as popular as our FlyAway service between
LAX and Van Nuys Airport.
From March 15 through March 31, all riders who take public transportation to Union Station (Metro Rail and buses, Metrolink, Amtrak, DASH, municipal bus systems and taxis) are entitled to a free roundtrip ticket on the FlyAway service.