SOMEONE’s never heard of Robin.
runs and hides
Seriously…he’s…far from.
The Golden Age/Earth-2 Batman was married to Catwoman.
Recently, he’s been involved with, or flirted with, Sasha Bordeaux, Wonder Woman, Catwoman (again)…
Then there’s Vicki Vale (although, I can’t quite determine if they were romantically involved before the first movie), Poison Ivy (there was the mind control, there, but she needed to seduce him first)…No doubt others that I’m blanking on.
I seriously can’t think of a version of Batman that’s asexual, rather than just unable to maintain a relationship, and/or involved in stories that his romantic life is generally secondary to (unlike Superman whose relationship with Lois - or Lana, or Lori - is often the central point of the story).
Comics, I’ve already covered…
The Adam West TV series, the tension with him and Catwoman was still there.
The old animated TV series, ditto - plus a handful of civilian women.
Justice League Unlimited has been using the Wonder Woman flirtation. Pre-Unlimited Justice League didn’t bother with any romances other than the John/Shayera plot - even the Superman/Lois relationship which is generally more central than any of Bruce’s flings.
The Batman makes the Catwoman/Batman flirting a little more one-way than the others, but the episode that introduced her involved Bruce lamenting that he couldn’t find a woman, and there may be something there with the female cop…
The movies are what you’re complaining about, and what I’m saying isn’t out of character for him…