Malaga Airport Buses.

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Their are various Buses available at Malaga Airport.
The go to many destinations, including Marbella Bus Station.

Malaga Airport to Marbella Bus.
The Direct Bus Service between Malaga Airport and Marbella Bus Station, takes 45 minutes. The Bus Service is operated by Portillo Bus Company. The fare costs 4 Euros, and you pay the driver directly.

You can call the Marbella Portillo Bus Service office on 952 764 401 and the Malaga Office on 902 143 144

Bus from Malaga Airport to Puerto Banus
Their is also a Bus Service between Malaga Airport and Puerto Banus. For this trip, many people advise to take the Bus to Marbella, and then take a 10 Euro Taxi ride on to Puerto Banus.
This Website, may help - Go Marbella.