They've been doing thia dance for 80 years now. Can we talk about the attraction? And what makes their relationship tick? Why are they into each other?
The answers really depend on which version of the myths we're talking about. The Burton films have one , The Nolan films have another, BTAS has one take, Gotham the series has another etc.
Its a bit difficult to answer imo, given that there really aren't definitive versions of these characters.
I guess if there's one constant in the tv and film realm , its Batman's desire for Catwoman to "go straight" though the question always is "to what end?".
Bruce isn't Clark Kent, and his demons make it difficult for him to truly trust, settle down, or truly be a spouse/partner who'd be there to support her emotionally.
So, if we're playing armchair psych, maybe its her "unavailability" that draws him to her.
Deep down, he knows he can't or won't truly commit to someone, so he's drawn to someone who's basically always unavailable and elusive .
She's shifty, dangerous, etc, so he knows he can never truly trust her 100 percent, nor could have ever really commit to her and take the risks involved in any committed relationship.
But since he fears those things , he goes to someone unlike Vicki Vale, Silver St Cloud, Julie Madison, who won't demand of him a true commitment and emotional stability.
And that's not even counting his own commitment he feels to Gotham, his parents memory, his need to control etc.