In those two previous appearances, Kathy Kane was a socialite that Batman felt was playing at heroine to try to figure out his identity, and, in those appearances, Batman tried as hard as he could to discourage Kathy from permanently taking up the mantle of Batwoman.
That changed after she helped the World's Finest Team.
The trio keeps ahead of Batwoman (barely, including a visit to the Daily Planet by Batwoman, to see Perry White, Lois Lane and Clark Kent; as well as a Bat Cave).
The boys do manage to hide their identities from her, but Batman backs down on his objections to Kathy being Batwoman.
Better still, this tale has been reprinted many times, including in the Giant World's Finest Comics #161, the second World's Finest Comics Archives, and in the first Batman and Superman in World's Finest Comics Omnibus and tradepaperback.
Bat-Mite, Ace the Bat-Hound, or her niece, the Teen Titans' Bat-Girl) or even with Superman fighting Luthor in World's Finest Comics!