Belongings left on HavaIST airport shuttle buses as generally returned to the HavaIST desk at your routes’ respective airport. If you’ve lost something during your trip, notify the Lost and Found Department immediately through the Call Center at 0850 888 33 34.
In general, they throw out perishables, hold valuables and currency in an airport safe, and return identification to the proper authorities within 5 days. It is, however, possible to have items returned on the same route you lost them on. You can view more details in Turkish on their lost good page, or use Google Translate on the link. Their FAQ page simply mentions calling the number above.