But . . . why would she seek help from merely Bruce Wayne if she didn't know he was Batman?
When she had said "Time I finally reached out . . . to him," and then tells Bruce "I'm sorry I haven't contacted you sooner. But the mess I'm in . . . I guess I just wanted to get out it myself. I didn't want you to swoop in and save the day.
But now . . . this has gotten out of hand."
Why would she expect
Bruce Wayne to suddenly "swoop in" to this mess with the Penguin, "Mr. Blonde", etc. unless she already knew Bruce was
Batman?
It really doesn't make sense unless she knew Bruce was Batman
(though, unfortunately, Bruce at that time didn't know he had been Batman).