I'm just saying that it wouldn't be as easy for Booster to open up to someone he feels he failed repeatedly.
Well, it could also be argued that he wouldn't have been easy for Booster to open up to Bruce about it, but because Bruce confronted him with his knowledge of it, he did. The same scenario could have happened here with Babs.
I suppose what I'm saying is which writers' version of Bruce do you think won? The Bat God or the good friend?
I only read the "Bat God" story in part, and on the old scans_daily, so I'm not sure I fully grasp the concept when people talk about it. I think a well-written Bruce, who is considerate of his friends (and considering past conversations between him and Babs about the shooting, I think he would realize what the considerate thing to do here would be) would tell Babs.
What would make a better story: her knowing but not saying anything for her own reasons or her reaction when she does find out?
Definitely the latter option. There's not as much room for conflict or interesting character interaction in the former.