Joker's obsession with Batman is initially the standard "game," matching wits, etc, but once she figures out that Batman is a woman, the obsession shifts to Bryce herself, to soulmates, and getting that damn batsuit off.
Joker is also super brash, vulgar and generally ""unwomanly.""
[this is based on an actual line from the batman (2004) where Bruce replies to Barbara asking when she would get to see the man behind the bat, with "who says I'm a man?"]













