The 43-45 arc of Gotham Knights imply heavily that Jim knows Bruce Wayne = Batman. Issue 44, iirc, has Jim pestering that Batman's not in town and unreachable, and when he goes home he finds Babs telling him that Jason Todd, whom she tutored, has died. It's been a while since I read that scene, but Jim has an expression there that says clearly he can see the link between the two.