Now, I love Babs as Oracle, and Cass as Batgirl, but that doesn't mean I have no love for Babs' time as Batgirl. Especially these stories.
This first story is Flawed Gems (Secret Origins #20), by Barbara Randal. It's an old friend. We go way back (It's also a very large comic, also including the origin of the original Dr. Mid-Nite, so I've kept the pagecount kosher)
This second story is Folie a Deux, from Legends of the DC Universe 10-11, by Kelley Puckett and Terry Dodson. It's a recent find, one I bought just a few weeks ago, and I'm kicking myself for not knowing about it sooner.
Cutting out a lot, much about Jim starting to have suspicions about what Babs is doing with her free time... he's not an idiot. He pretty much knows, he's just not sure how to feel about it. It's a slightly different take on her background, so Babs is starting some "Batgirl" stuff while still in college.
The private lessons seem to be going well, but Jim finds out about them, and decides it's finally time to speak up and put an end to things.
But then he gets shot while trying to stop a robbery... while Batgirl's watching...
The bad guys seem to have an inkling that things have gotten out of hand, and settle for tying up our heroes.
She does it, using everything Batman taught her about misdirection, and then carries Jim to a hospital herself... then "Batgirl" vanished.