Bruce Wayne, one of the richest most powerful men in Gotham, spends his nights beating criminals to a pulp with his bare hands. Kate was wrapping her head around this realization as she was led down into the Batman's secret HQ under Wayne Manor, appropriately built into a cave. The huge cavern, filled with gadgets, vehicles, computers, and souvenirs from past triumphs, made her little hidden garage look modest in comparison. Even their Batarangs featured a fancy spring-loaded folding design, compared to Kate's which were nothing more than sharpened shards of steel.
There was way more people involved than she would've thought. She knew there was a Robin and a Batgirl, she didn't know there were multiple of both. When she thought about it, Wayne being the Batman kinda made sense. Wayne has the motive and the means, and it follows that his sidekicks would be people close to him. Most of them she either didn't know or only knew about impersonally. But just looking at them she could believe they were either masked vigilantes or gym rats. Damian looked too young, but if he was the Batman's son maybe he had metahuman powers or something. The only one she never in a thousand years would've guessed was Steph. There was a moment when all Kate could do was stare and blink. No matter how hard she tried to imagine it, she just couldn't see the blonde cupcake jumping off rooftops in the middle of the night. Does this mean the only reason they were friends was because Steph was keeping an eye on her? The more she thought about it the less she wanted to, so she just played it cool like she always did. "I didn't know you were such a badass, buttercup. Maybe you could take me for a ride in the Batmobile sometime."
Apparently at least Wayne knew her identity. She knew she would get the Batman's attention when she put a big red bat on her chest, but she didn't think he'd figure out her identity so easily. After all, Kate had years of practice hiding who she really was. She wondered what else he knew about her, not much she hoped. On the flip side if he knew and didn't stop her, he must trust her to a degree. Having the Batman as an ally is pretty damn handy. Maybe he could introduce her to Wonder Woman.
The greetings didn't last long (she didn't even get most of their names) since there was business to attend to. Icy business. Before she had time to really grasp the fact that the Batman and his cohorts just revealed their secrets to her, he was giving them a sitrep and telling them to suit up. Kate wasn't sure what they were expecting from her, but she wasn't about to join their militia. Last time she enlisted in something she was kicked out for telling the truth. "I'll lend a hand this time. But, no offense, I'm not about to join your club."