That can't be easy for him to deal with, stepping into a situation where there's people who've had years of various kinds of history with him! It's funny, through her conversation with Jason, Bette's aware that Batman is here, and that he doesn't recognize anyone, but she's never known that Batman and Bruce are one and the same, so finding Bruce and having him just be like, "Cousin who?" is going to mess with her in so many delightful ways.