Quote Originally Posted by Lonewolf36 View Post
The part that confuses me is when Kara tells Kate that Clark and Bruce are "friends actually frienemies" does that imply that a Bruce/Batman exists on her Earth are Superman/Batman previously crossed Earths.
Kara's Earth has a Superman (obviously) and its own Batman/Bruce Wayne.

She actually made a hilarious but indirect reference to him in her show when meeting James as Guardian. Saying masks were for that other city and another time when saying her cousin often teamed up with a hero who used gadgets. So Bruce has indeed been referenced a handful of times as existing there.

It's also why she put two and two together. Chances are as per the norm almost all of Bruce's family are in the hero business on her Earth so meeting his cousin was easy for her to assume who Batwoman was.