Board Thread:DC's Legends of Tomorrow discussions/@comment-9346948-20180410010248/@comment-27700324-20180706065002

Exactly. Basically she is inspired by Batman's first mission to defend Gotham in the series finale of Gotham and we see her seeing Batman only during her debut in the crossover, but then Team Flash or the Legends arrive on this unknown Earth and have her come with them. (Because they need someone with her military strategy to defeat the latest threat to their Earth) So as she is feeling lost due to being ex-military and without a goal and seeing this extroardinary Bat figure saving her city, she goes with our team of superheroes from Earth One. Seeing that others do need her help, she decides to don the identity of her inspiration as Batwoman.