While Batman might be famous for being a loner, he's had many loves throughout his life. From Catwoman to fan-favorite characters like Talia Al Ghul and Andrea Beaumont, Bruce Wayne has had a long, varied love life, even if many of those relationships didn't end well.
I 2006, Jezebel Jet first appeared at the start of Grant Morrison's run in Batman #656 by Morrison and Andy Kubert. The run began with the "Batman and Son" story that introduced Damian Wayne and reintroduced Talia Al Ghul as a potential villain for the Dark Knight. With the topic of past romances reintroduced, Jezebel Jet entered with perhaps one too many things in common with Bruce Wayne.
With Alfred believing Bruce needed to get more in touch with his "playboy" persona, Bruce strikes up a conversation with Jezebel Jet, part of Mtamba's ruling famly, at a fundraiser in London. The two flirt a bit before Bruce's mask slips, revealing his distaste for the poverty and injustice in the world. Jet declines Bruce's phone number initially, citing that she didn't want to become another "Wayne Girl."
After a few more encounters, Bruce's dual identity starts to get in the way of his time with Jezebel. A charity skydive is interrupted when the Bat-Signal joins them in the sky. Bruce makes an excuse about getting the trajectory wrong when deploying his parachute, and lands at the GCPD ready in full costume.
By Batman #672 by Grant Morrison and Tony S. Daniel, these small moments have turned into rumors of marriage. Alfred asks if there's any truth to them and, surprisingly, Bruce does not refute the claims. A kidnapping leads to Bruce taking their relationship to the next level, as he screams that she was right about him wearing a "mask" while beating the kidnapper, leading Jezebel puts two and two together and realizes Bruce Wayne and Batman are one and the same.
The truth about Jezebel Jet is revealed in the "Batman R.I.P." storyline, which shows Bruce so comfortable with Jet that he casually enters a room with her while still half in costume and even walking her through the Batcave. When Jezebel tells Bruce about an invitation to the Black Glove's "Dance Macabre," Bruce shows her the case he's been building against them.
Jezebel sees the words "Zur-En Arrh" on the Batcave screens, which Bruce apparently can't, and says them out loud. This leads Bruce's mind to collapse and retreat into a backup persona -- the Batman of Zur-En Arrh. After Jet is kidnapped by the Black Glove and taken to Arkham Asylum, Batman, still in his Zur-En Arrh persona comes to rescue her.
Trapped by the Black Glove, Jezebel Jet reveals herself to have been a part of the organization all along. She used her relationship with Bruce to get closer and closer to him until he would reveal his secret, giving the Black Glove the opportunity to finally take him down. However, Batman already knew that Jet was not in love with him. As Batman takes down the Glove's goons, he recounts the most intimate and personal details of her life and tells her that he too was only pretending to be in love.
Though Jet managed to escape prosecution through diplomatic immunity, Talia's Man-Bat army hijacks her plane. It was later revealed that Talia had her beheaded, leaving her head for Batman Inc. to find. While it may seem that neither of them loved the other, it appears Talia may have grown a little jealous of her ex's rather complicated love life.