Questions & Answers about Güle güle, yine gelin.
It comes from the verb gülmek, which means to laugh or to smile.
Historically, güle güle is related to the idea of go smiling or go happily. But in modern Turkish, you should mostly learn güle güle as one fixed farewell expression, not as something you need to build from scratch each time.
Because güle güle is an idiomatic fixed phrase. Turkish often uses repetition in set expressions for rhythm, emphasis, or a natural sound.
So here, the repetition is just part of the expression. You normally say güle güle, not just güle, when using it as a goodbye.
This is a very common learner question, because it works differently from English goodbye.
Güle güle is usually said by the person who is staying to the person who is leaving.
So if someone is leaving your house, shop, or office, you can say Güle güle to them.
The person who is leaving more often says hoşça kal or hoşça kalın to the person staying.