January 2011. Can one even call this "flirting"? Bruce Wayne and Selina Kyle do some heavy lifting in the first issue of Grant Morrison's BATMAN INCORPORATED.

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January 2011. Can one even call this "flirting"? Bruce Wayne and Selina Kyle do some heavy lifting in the first issue of Grant Morrison's BATMAN INCORPORATED.
March 1984. Poor Jason. Everyone knows it, but you can't just say it.
October 2006. Jealous much, Selina? This scene from BATMAN AND THE MAD MONK #1 is set early in Batman's career, inserting into the "Year One"/LONG HALLOWEEN period a modern version of some of Batman's earliest published adventures (in this case DETECTIVE COMICS #31–32) — including Bruce Wayne's engagement to Julie Madison, the Chanel wearer to whom Catwoman alludes:
He's just so emotionally articulate.
May 1983. TFW both your girlfriends lecture you about your reluctance to commit before going home with each other, in another scene from DETECTIVE COMICS #526. (It's not actually clear how Talia got to Wayne Manor earlier in this story, but she presumably has her own transportation, so I have to assume she's in Selina Kyle's car because she's going home with her.)
April 1983. How the Earth-2 Batman and Catwoman finally worked it out, in Alan Brennert's exceptionally poignant "The Autobiography of Bruce Wayne" in THE BRAVE AND THE BOLD #197.
March–April 1978. Besides Selina Kyle and Talia, the other woman once commonly suggested as endgame for Batman was Silver St. Cloud, whom Steve Englehart introduced in DETECTIVE COMICS #469, and who then made her exit in this scene in DETECTIVE #476. She didn't return until years later, but what caught readers' imagination about her was that she seemed an ideal match for Bruce Wayne, not Batman — she was smart, affluent, and socially active, a woman of Bruce's class, but no shallow dilettante. However, when Silver realized Bruce was Batman, she couldn't stand the prospect of being caught in his demimonde of madness and violence, which he will never really leave.
February 1986. In BATMAN #392, Batman takes Catwoman out for a romantic dinner — in an alley next to the garbage cans. (Richest man in Gotham, mumble, mumble.) He does have the courtesy to refer to himself as the tramp, at least:
December 1980. While this cover does sum up Dick's reaction to Talia in this storyline, Bruce and Dick are actually already at odds even before she shows up: Dick has just recently returned to Gotham after dropping out of college, and Bruce is so pissed about it that he's more or less giving Dick the silent treatment. Also, Talia enters this story by killing someone right in front of Batman and Robin, and she then spends a lot of this and subsequent issues acting very squirrely, so Dick's antagonism isn't entirely unreasonable.