I have biked to LAX many times. I usually approach from the beach area: Ballona Creek bike path to the beach, then up Westchester Parkway to In-N-Out Burgers, and then Sepulveda to 96th Street (the continuation of Century Blvd on the lower level entrance). There is a bike rack right outside the arrival level of Terminal 1. Security doesn't seem to be an issue as there are plenty of bikes parked there every time I go; and of course the Airport Police stands right there by the vehicle entrace. It does appears that many other people do the same... bike to LAX for quick short trips without luggage.

I have no idea what kind of bicyclists you are but I will assume you are moderately intrepid... meaning you can confidently negotiate shared lane on less busy streets and have no problem riding on busy roads with marked bike lane. If you are starting from Pasadena, I suggest the following routing:

Take the Gold line from Old Town (you can bring your bike on Metro on weekends) to Downtown LA Union Station

From Union Station, take Broadway or Spring St to Venice

Take Venice (which has a bike lane) to Overland

Take Overland to Ballona Creek bike path

Take Ballona Creek bike path to Lincoln Blvd near Playa Vista

Take Lincoln (which has a bike lane, although be aware of steep grade) to Layola Blvd and then onto Westchester (which has a bike lane)

Eat something at In-N-Out for making it all the way there

Take Sepulveda to 96th lower level approach to Terminal 1 (don't go up the departure ramp)

http://maps.google.com/maps?f=d&sour...&z=15&lci=bike

Edit: Note that some mapping service will tell you to take Ballona Creek bike path from Downtown Culver City instead from Overland. Don't do that... the Ballona Creek bike path near Downtown Culver City is closed right now due to Expo line construction. Follow the route I highlighted for you and it will be open 100% all the way this weekend.