I've never read more than a handful of Detective Comics and other pure Batman titles. I think my first introduction to Batman was on the Superfriends and his Filmation shows, as a guest on Scooby Doo, from stories on 45 records, from Worlds's Greatest Superheroes newspaper comics (my grandpa used to cut them out and save them for me, I still have some of them), and so on. Later there was Burton Batman, Schumacher Batman, Batman '66 on Nick at Nite, Batman Elseworlds stories, Batman vs. Predator, BTAS, all the later Batman cartoons, animated Batman movies, the Arkham video game series, Nolan movies, Snyder movies, the Reeves movie, and God knows how many I'm forgetting.
Point is, Batman has been part of my life for as long as I can remember but he's always been pretty malleable. Maybe if I read the comics more I'd have a more definitive take on what Batman must be.