Actually, it would be really cool if that story ended with Booster visiting Barbara to tell her himself and explaining why Bruce and Dick never told her.
Booster: "So try not to be mad at them. I think they wanted to tell you more than anything, but even I have trouble dealing with the consequences of time travel and thinking constantly about the what if's."
Babs: "Ted was right about you."
Booster: "Ted? He talked about me?"
Babs: "Yeah, I asked him on one of our dates why he spent so much time with a sell-out like Booster Gold and he told me your heart is as big as Superman's, you just don't like to show it off. He was right, you're a good man and my hero. Thank you for telling me Michael."
Booster: "Thank you Barbara." *inner dialogue* "Thank you Ted."