Los Angeles International Airport: For most visitors, rent a car or take a rideshare directly to the specific part of Malibu where you are staying; Malibu is a 21-mile-long coastal city, not a compact center. Allow roughly 45–90+ minutes to central/eastern Malibu depending on traffic, longer for Point Dume or Zuma; rideshare fares can easily run about $70–140 before surge and tip. The cheap option is Metro: take the LAX/Metro Transit Center connection to the K Line, transfer to the E Line for Downtown Santa Monica, then Metro Bus 134 along PCH into Malibu. Budget 2–3 hours and roughly $1.75–3.50 in Metro fares; it works for a light-packing beach day, not for efficiently seeing several beaches.
Hollywood Burbank Airport: Use a rental car or rideshare; it is not meaningfully better connected to Malibu than LAX. Expect about 1¼–2½ hours by road depending on the time and destination in Malibu, and a costly rideshare. Public transport requires multiple changes through Los Angeles and Santa Monica before Metro Bus 134, taking roughly three hours or more—only choose it if price matters far more than your day.