In Batman #139 (Feb 1961), the creators try to improve the supporting cast of the Batman “family” by adding Bat-Girl. Betty Kane, the niece of Kathy Kane, discovers her aunt is actually Bat-Woman and decides to help out with crime-fighting. Batman encourages her to train her sidekick as a stalling tactic, but it actually seems to take and she joins the dynamic “trio” on adventures and to make Robin feel uncomfortable.
This version of Bat-Girl only lasts for a few adventures before both Bat-Woman and Bat-Girl are “retired” to make way for a more serious version of Batman.