From Izmir Adnan Menderes Airport you can reach Çeşme by using "Havaş"s. During the Day buses from Izmir to Çeşme leave every 30 minutes, but during the night every hour.
The last service from Izmir to Çeşme is 23:00.
From central Izmir to get to Çeşme you can ride on the buses from Izmir's bus station. It takes about 1 hour and 30 minutes. Another choice is the buses from Üçkuyular. The Üçkuyular buses take 30 minutes to arrive at Çeşme. There is also direct bus service from Istanbul to Çeşme and Alaçatı.