He noticed the shift easily enough - and it was interesting, because that wasn't the typical response, but if she was from another universe (or possibly just another timeline?) and he knew her at all well...

His voice lost a bit of the edge it had when he was probing her, though now had gained a different one. Thus far there were four people he'd willingly granted access to the cave - Alfred, Dick, Tim, and Barbara. That he'd allowed her down - that he'd shown her down, according to her - was profoundly telling. The fact that she claimed to be a superheroine was also telling, because she wasn't acting as though she worked directly for him. That made sense, it was difficult to imagine him having a princess as part of his team.

The voice he spoke with was halfway between his two personas - too dark to be Bruce Wayne's normal self, but still with much more charm than Batman ever really displayed. "I'm not sure about that. I don't know if I could resist showing off for you, even if it wasn't much." He's still flirting, though at this point it's half-automatic.

She knows him, but he doesn't know her. He doesn't know how well he knew her, but apparently well. She'd been to the cave. She was a hero. What else?