Think about the fact that her getting shot didn't have anything to do with her as a person, but only to do with who she was in relation to her father and Batman. She wasn't shot because she was Batgirl and a thorn in his side, she was shot because of how it would affect the men in her life.
Then Rip Hunter gets Booster to try and prevent the shooting (knowing full well he can't) in order to prove to Booster that he can't save Ted. Again, that has nothing to do with Barbara and she had no say in the matter.
And then with Bruce and now here with Dick, you have Booster and Barbara's friends discussing what happened as if it had nothing to do with her.
The entire sequence of events implies that she's not a person, but a prop to be passed around in order to affect the story.
Having enough respect for Barbara as a person to tell her about what happened, to include her for once in something that intimately involves her, should be a god damned requisite for doing a story like this.