If you are short of time or are travelling in the dead of the night then I believe that your only option is to take a taxi.
If you have plenty of time during the day or early evening.In addition to Havas there is a Belediye bus which runs at two hourly intervals from the bus station to the airport, number 102 if I remember correctly.
You also have the option of catching the local bus to Alanya/Manavgat. These buses, run very frequently during the day, do not go into the airport but will drop you at the taxi rank at the junction of the main road and the airport turning.
Apart from agreeing with KKOB's taxi price estimate I cannot advise on the bus prices.