It is interesting to note that before the new 52 and the more or less final reinvention of Bette Kane, and now stranded in her yeaaaaaars
at West Point -
Bette was twice imagined/reimagined as the successor to Batwoman.
1) in the old silver age stories that Alfred wrote about Dick and Betty inheriting the titles of Bat Man and Woman
2) in a circa 2000 Titans/Tomorrow storyline, Bette is reimagined as both a lover to Tim Drake and the person who becomes the new Batwoman.
I don't have the links or pictures but they've been shown many times in these forums.