There is no direct bus from S'Arenal to Palma Airport -- you will need to change in Palma -- so a taxi is the easiest option for airport transfers, especially with luggage.
Once settled, local buses are frequent and cheap. The number 25 runs along the Platja de Palma to Ca'n Pastilla and on to Palma every ten minutes, with a single fare of around one euro. The flat beachfront promenade also makes walking and cycling between the resorts along the bay straightforward.
A limited bus service runs east to Manacor, Porto Cristo, and the Coves del Drac, making it possible to do a day trip to the caves without a car.