Batman: The Animated Series is considered a seminal adaptation of the Dark Knight. Unlike many other children-oriented projects, the show's mythology had an impressive longevity, being part of a universe comprised of Superman: The Animated Series, Justice League Unlimited, Batman Beyond and others. Having that many projects covering a long span of time meant fans had the opportunity to experience almost all of Bruce Wayne's life journey.
He evolved from a relatively young crimefighter into a father figure. From there, he became a member of a superhero team and decades down the line found himself mentoring a new Batman. With such an all-encompassing coverage of his development, some fans may feel they know Bruce Wayne quite well. However, there may be a pivotal moment in his life that not many are aware of, and it involves an outlandish multiversal conflict in the Teen Titans Go! universe.
Brainiac's Multiversal Conflict
During its seventh season, Teen Titans Go! had a four-episode crossover event with DC Superhero Girls dubbed "Space House." The crossover saw the Titans and the Superhero Girls go on a mysterious space vacation. They all stayed in a space-traveling house controlled by Brainiac, which led them to the villain's skull ship during the event's final chapter. There, the heroes found many other crimefighters (and villains) from the multiverse vacationing with each other, including — as shown in the picture above — Joker from Batman: The Brave and the Bold, the Penguin and , of course, Batman from Batman: The Animated Series.
As for the reason behind them being there, they were "collectibles" for Brainiac, who managed to lure them into his ship by promising some free downtime. What made the Dark Knight's role in "Space House" more unexpected was how he was happily hanging out with the Clown Prince of Crime. While his appearances in the event are brief, Batman does get to see some action near the end of the fourth episode, as he helps the Titans and other multiversal characters take down Brainiac before he can fulfill his new planet-destroying hobby.
Given the absurdist nature of Teen Ttians Go!, we shouldn't necessarily take Brainiac's ship as a canon destination for the DCAU's Bruce Wayne. However, just for the sake of speculative fun, it's worth noting that the Batman shown in this episode features the design from Batman: The Animated Series' first incarnation, and not from its 1997 continuation, The New Batman Adventures, which had different visual style akin to that of Superman: The Animated Series.
Assuming this appearance is canon (which, again, it likely isn't), it would mean that, by the time The New Batman Adventures came around, Bruce Wayne had already vacationed with his greatest enemy somewhere in another universe.