Did batman ever time travel?

Yes, Batman has traveled through time on several notable occasions! One of the most famous is in Grant Morrison's story arc where Batman is sent hurtling through time by Darkseid's Omega Sanction at the end of Final Crisis, forcing him to survive through different eras of history — this is explored in the series Batman: The Return of Bruce Wayne, where Bruce Wayne must fight his way back to the present through various time periods including caveman times, the pirate era, and the Wild West. Time travel has also played a role in various Elseworlds and crossover events featuring Batman. If you're looking for a great read, Final Crisis and Batman: The Return of Bruce Wayne are the key stories to track down!