Right, but if Batman can know about it and not mess up the timeline, there's no reason Barbara can't considering she is the one the whole thing most concerns. And given past conversations and she and Bruce have had about how she felt about the whole incident, the decent thing for Bruce to do would be to inform her about it. Both she and Bruce know how to keep a secret.
Besides, I think Babs and Booster are overdue to get to know each other, not only because of this whole thing, but because of their relationships to Ted Kord. After all, Booster wound up trying to prevent the shooting in part because he was trying to prevent Ted's death. And Babs and Booster were two of the three people who actually tried to help Ted right before he was killed. Both Ted and Bruce trusted Babs, and that should be good enough for Booster.