Really? I've been having the exact opposite reaction.
Babs has been coming across as barely competent and totally unprofessional to me. Really, the only part that seemed at all like Bruce/Babs to me was this one bit where he mentions that he'd set up a satellite cave on the Asylum grounds, and she was all "You've got a Batcave on Arkham Asylum?"
"It's -me.-"
I laughed.
Other than that, I found myself wondering when the collected folks of S_D were going to rise up and go grab their pitchforks.