Stephanie quickly introduced herself as Batgirl and informed Kara that she had discovered Toyman was holding the Kryptonite Man captive and torturing him, when one of the Toyman's robots overwhelmed her and Catwoman and put them in this predicament. The two girls agreed to go investigate, leaving Catwoman behind.
On Stephanie's instruction, they entered the place through the sewers. She told Kara that this was because Batman had always taught her that good guards took rooftops and windows. Kara revealed she knew this piece of teaching too, as she had also trained with Batman on earth. They bonded over this, Supergirl reminiscing that Batman had taught her to be human. Stephanie replied he had taught her how to be a hero. Kara admitted she missed Batman, and after a pause, Stephanie admitted the same, but insisted that Batman lived on in other ways.
Kara was prepared to charge in optimistically to take down the villains, but Steph was more cautious. Kara jovially asked her, "It's the first Supergirl-Batgirl team up, what can go wrong?" And Steph made sure to give her a sarcastic "You were saying?" when the pair was overwhelmed by Toyman's robots. However, Steph held her own, and Kara smashed the head robot's head in. But as soon as Kara declared the mission to be in the bag, Mr. Freeze appeared with one of his guns.
Stephanie quickly leaped in front of Kara and threw Batarangs that disabled the weapon. When Kara assured Steph she could have taken the ice, Stephanie shrugged and said she had to pull her weight in the team up, because Kara "took out Toyboy and I owed that little jerk".
However, the fight was not over, as Toyman attacked the girls with a huge composite Superman/Batman robot! Stephanie had Oracle call in Superman and Batman, but panicked in the robot's clutches. She panicked even more when the robot dumped Supergirl into it's mouth, yelling, "SUPERGIRL!" after her new friend!
Batman made the robot drop Stephanie and Damian rescued her before she could splatter all over the ground, but while doing so he made a snide remark about her weight and called her "Fatgirl". Supergirl was rescued and the day was saved. Supergirl later chastised Damian for insulting her new friend, picking him off the ground by his cape and telling him he "shouldn't call girls fat! You shouldn't call anyone fat!" while Stephanie looked on with her arms crossed.
In Batgirl (third series) (8), when Ra's Al Ghul shut down all of Gotham's communications, Steph sent a note to Oracle informing her who was responsible. Oracle quickly called in Kara, codename "Bluebird" to trash Ra's sattelite and restore normalcy in Gotham. When Steph heard this, she asked if Kara was still on line. She told her, "Thanks, Supergirl!" and Kara responded, "Anytime, Batgirl!"
In Batgirl (third series) (14) Kara comes to visit Steph for a fun night on the town. They spend some time on the Gotham University campus and Kara is fascinated with the college lifestyle ("All the excitement, the social intrigue…what should we do first…keg party? Pillow fight?”) and eventually they settle on seeing a movie. However it goes wrong when due to a slip up at a local lab, vampires come out of the screen and start attacking Gotham. Kara and Steph team up and take them down, spending the Friday night defeating Draculas left and right. Eventually they get some time to themselves when Kara discovers there is an emergency back at Metropolis, and as she leaves the two girls vow to hang out again soon.
More information on Kara here!