Alien worlds are now a regular location for Batman stories, as can be seen on the cover of Batman 116 (June 1958).
Moldoff and Paris give Batwoman a new secret identity in this story, as she adopts a blonde wig to go undercover while pursuing the Funny Face gang.
Batman and Robin spot her in her disguise, and head to Kathy Kane’s Batcave, finding the blonde wig, and realize what she is up to. Of course he is determined to stop her, as fighting crime is “too dangerous for a girl,” and of course she does not listen.
But the gang see through her disguise as well, and Batwoman almost gets killed by them. Batman intervenes, and then tells Batwoman once again to retire. She points out that, had he not saved her, she would have had to stop being Batwoman, being dead and all. Batman sounds genuinely regretful that he saved her life.
The cover story, by Finger, Moldoff and Paris, starts off as Batman and Robin fly through a hurricane and wind up in some alternate dimension. Or an alien world. Or just somewhere weird.
The kingdom they wind up in first believe them to be a threat, as they are menaced and attacked by winged bat-people, whose outfits resemble Batman’s. But he fights off their incursion, and so the people begin to trust him.
Using the Batplane, Batman ignites a coal seam, creating a barrier of fire to keep the bat-people at bay. The explosion also sends the heroes back to their own world.