She'd been prepared to move, to dodge the bullet, but before he even lowered his arm she knew she wasn't going to have to. But she wasn't expecting him to do was...sit down. The last time she had ran into Joker in her world, he'd run for it. Either the time difference between them made things different, or this was not the same Joker. If anything...he seemed more insane. Was the possible?
Batman would have her head if she engaged Joker alone. She knew, right away, she could take Joker down. But then what? Hand him to the police? He would probably escape, and kill them in the process. And she wouldn't kill someone else, not again.
This was the man that made so many people panic. That had killed Jason, leveled Barbara's life, and now had done this to Terry. "Eight." she answered. If you counted everyone who had been associated with Batman, himself included, there were eight that she knew of.
She didn't know what to do with herself at this point. Even if she could just get one good, satisfying punch in...maybe it would be worth it. "And his name is Batman." which Batgirl still found weird. There were two Batmans, not Bat Brat.