It is recommended to rent a car to explore Malibu as public transportation options are limited. The estimated cost for a car rental is $50-$100 per day depending on the type of car. The total travel time for this itinerary is around 6 hours if you start and end in downtown Los Angeles.
If you have more time, consider visiting the Adamson House and Malibu Lagoon Museum or the Point Dume State Beach and Preserve. If you have less time, you can skip the Getty Villa and spend more time at the beaches. Don't forget to bring sunscreen, hat, and sunglasses as it can get very sunny and hot during the day.