So, back in the day, Jor-El was kind of dopey:
Well, she discovers Batman & Robin's secret identities [SPOILER ALERT--Nope, she doesn't], and she's got a grand plan to figure out who Superman is!
Well, I guess there's absolutely nowhere you can take Batwoman where she'll be frightened to follow. Except...
From World's Finest Comics #90 (1957)