Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Yogyakarta to Bangkok as you normally would.
Yogyakarta Adisutjipto (JOG), located 6.8 km from the city centre, is the airport you fly out of when you book flights from Yogyakarta to Bangkok. 2 airlines have flights from Adisutjipto to Bangkok on a regular basis. Booking flights from Yogyakarta Adisutjipto to Bangkok should not be difficult; the airport handles an average of 0 outbound flights to Bangkok per day.
Due to the rapidly changing circumstances due to COVID-19, airlines like Singapore Airlines and AirAsia flying from Yogyakarta Adisutjipto to Bangkok have implemented new flexible cancellation policies.