Check out Superman's impression of Batman from the 1996 Superman: The Animated Series episode "Knight Time."
The episode sees Bruce Wayne under some sort of mind control leaving people to believe there is no more Batman in Gotham City.
So for two weeks there is no sign of Batman, but then Gordon lights up the sky one last time in hopes of The Dark Knight answering the call, but little do they know it's SuperBatman and Robin!
If you haven't seen the episode or just haven't seen it in a while, it's a really cool depiction of what it would be like if Superman was Batman. It's especially cool when Superman confronts Batman's villains and the ensuing (albeit one-sided) fight that takes place.
Superman: The Animated series ran until 2000, with episodes available to be watched through YouTube or Amazon Prime.