Yes....there are buses that go to Malibu from LA...check this out for the route to take:
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It depends where in LA you are starting, but the Metro Express 534 bus goes from Santa Monica all the way up Pacific Coast Hwy to the top of Malibu.
Right on answers from both replies. In my opinion, the Getty Villa is a must see for anyone wanting to see Malibu or the areas nearby. Reservations are free, but must be made in advance. If you decide to visit the Getty Villa, do not confuse with the Getty Center in the Westwood Area of Los Angeles. You can get to the Getty Villa via public transit! Metro Bus 534 as mentioned with a stop at Coastline Drive and Pacific Coast Highway directly across from the Getty Villa entrance. Passengers exiting the bus at PCH (Pacific Coast Highway) and Coastline Drive must have their Villa admission ticket hole-punched by the driver before exiting the bus in order to enter the Villa. Beautiful setting, great displays of antiquity, as well as a fabulous pool garden.
Yes, the ocean coastline is beautiful, surfer's point at the Malibu Pier to watch the surfers ride the waves is a great attraction. Good beach as well, and in the Zuma Beach area is a great PCH (Pacific Coast Highway) Fresh Seafood restaurant with lots of locals enjoying the fried or called "Neptune's Net" with outdoor casual benches. Everything from lobster to calimare. See my VT Malibu page for the Getty as well as the Neptune's Net and other sites. "MALIBU: CELEBRITY PACIFIC COASTLINE PLAYGROUND" - Malibu by travelgourmet