Did bruce actually say somwhere that he didn't trust Steph to be Batgirl or anything else? Then what was that whole thing in Robin upon her return to Gotham City? Where he pretty much welcomes her back (and then in a contrived but still canon plot thread leaves it up to Steph to make sure Tim is ready to deal with the aftermath of Batman's disappearance?)
Yeah...either you missed or I missed something, but far as I know, stephanie received Bruce's blessing to fight crime with them. It was Tim in the end who didn't want her to continue being a crime fighter.