Intro: Well, here we go. A tale as old as time. As well as a very complicated one. I'm not sure if BatCat's the proper ship name for these two, but it's the only one I could find. And I had to, considering this is my preferred ship when it comes to the character of Batman.
Proof: What can I say that hasn't already been said? They've pretty much had romantic tension ever since Catwoman was first introduced in 1940 (as far as I'm aware). Most portrayals of this relationship have been the concept of "forbidden love", since Batman's the hero, and Catwoman is the villain, but sometimes she's an antihero, depends on who's writing the stories.
So instead of attempting to give you all the proof, I'm just gonna go over two personal highlights that stand out to me.
In the Injustice comics (yes, I know it's an alternate universe, but there's little difference between it and the proper canon, so screw it), Selina was on Batman's side through most of it. And when Nightwing died (oh, uh, spoiler, I suppose), she helped calm and comfort Bruce, as seen in the panel above. They have a few sweet moments in Injustice besides this one as well.
The next has happened more recently, with Batman proposing to Catwoman after the events of The Button storyline. From the looks of how things are playing out, it seems like Bruce might be quitting being Batman and honoring his father's final request by living a normal life. Of course, that's just my personal speculation on what's happening, but still. Also, I haven't seen what happens after he proposes, so... was it a yes or no? Still not sure...
(A/N: After further investigation, it is confirmed that she said yes.)
What I think: Like I said at the beginning, this is my preferred ship involving Bruce Wayne. I can't really say anything else. I don't ship it as much as others, but I still ship it nonetheless, and I feel like I have wronged myself by not bringing it up earlier.
