BabsDami

BabsDami is the friendship ship between Barbara Gordon and Damian Wayne from the DC Comics and DC Super Hero Girls fandoms.

Canon
Barbara wasn't very sure of Damian at first, due to how his spoiled attituded, and the way he treated others he saw as below him. Eventually they came to a more amicable relationship as they both fought crime in Gotham. When Damian was killed and his body was taken to Apocalypse, Babs joins the group who go to get him back. While wearing the Robin "R" to remind them who they were fighting to save.

DC Super Hero Girls
In the G1 DC Super Hero Girls web series, Batgirl gets tasked to babysit Damian in "Kid Napped." Something that neither of them were happy about. Along with the young Robin making things harder when he threw one of the batarangas at Batgirl before running out of the room, leading her to chase after him. Wanting to help her friends deal with shadow monsters rather than looking after Damian, she calls him a waste of time. Damian states that he doesn't want to waste her time either. Realizing that her words might have hurt Damian she tries to make up for it by offering to tuck him into bed and possibly read him a story to help him sleep, but Robin refuses. He then goes to put himself to bed so that Babs can go help her friends like she wanted.

Unknown to them, a pair of Shadow Creatures had gotten into the room to kidnap Damian. Batgirl finds the ransom note that they left, and rushes to Damian's rescue. When she arrives, she's not too surprised to find a freed Damian having everything under control. Having apprehended the two shadow villains who kidnapped him on his own. Still feeling bad for what she said earlier, Batgirl apologizes for what she said. She reassures him that she does see him as one of her friends and Damian also apologizes for the way he acted. He decides to let Batgirl tuck him into bed, even though he can't promise her that he'll sleep after words.

Harley Quinn (2019)
Barbara and Damian are two of the five Batfamily members to be featured in the 2019 animated series of Harley Quinn. Batgirl and Robin have been working together with Batman for awhile before Nightwing returns to re-join his father and mentor in his mission.

Moments

 * Lego DC Heroes


 * After the two got their drinks form Alfred, Robin and Batgirl were seeing smiling at each other.

Fanon
Due to the big age gap between the two, people tend to ship them as friends. That is why there are currently over 45 gen fanfics and only over 5 het fics on AO3. Even though Barbara forming romantic-like attachments to those who have served as Robin isn't something new, and there has been a small group who het shipped Damian with Stephanie Brown, people prefer to have her as another one of his big sister-like figures. Next to Cass and Steph. This could also have their DC friendship be featured as a familyship, with the two being members of the Batfamily. Since some of their interactions in kids cartoons had Damian acting like an annoying kid brother to Babs, who tries to either bond with him or makes sure that he stays out of trouble. Along with New Earth having the two as in-laws when Babs married Dick, one of Damian's adopted brothers.

Fandom

 * FAN FICTION