Story about a time traveller who became their own mother and father

It sounds like the movie Predestination, which is also based on a novel (see other answers).

The main character, a time traveler, is revealed to be a hermaphrodite. A Barkeep meets a man, John, that reveals that he was raised in an orphanage and as a girl. She had a child with a man she knew, but disappeared from her life.

The child, the Barkeep, John and Jane are all the same person, at different points in their own timeline.

So, the woman didn't meet a man she barely knew in a bar and have a child with them, but there is a main plot point about the character meeting a man in a bar.

This timeline image shows the loop of their life, plus their other identity:

• Next usage - Are 'third person singular pronouns' optional?
• Previous lord of the rings - Why did they take a Palantir with them when they left on the last ship going west to the Undying Lands?