When you arrive at the Aruba International Airport Reina Beatrix your only options for transportation are by Taxi, prearranged private or shared transfer or a friend or family pick up if you are not renting a car to drive yourself away on. In other words there is no Aruba airport shuttle, to the hotels or anywhere else for that matter for now.
There is no Uber, Lyft or any other transportation of its kind available on the island.
Public transportation option does not come into or by the airport itself, if needed you have to walk out to the closest bus stop.
Additional information, http://faqsaruba.com