In Arkham Knight's DLC "A Matter of Family", Robin is often trying to tell Bat-girl something, but always loses his nerve. By the end of the mini-story, Robin didn't get to say what he wants to say, at least not in my game. What did Robin want to say to Bat-girl?
I have not played the Batgirl DLC, myself. I think it is also difficult to speculate what a fictional character wanted to say, without the developers themselves telling us their intentions. But I speculate he was trying to (tell her he likes her/ how he feels/ ask her out), and here is why:
The Batgirl DLC is set before the main game. This is pretty obvious; Barbara Gordon was Batgirl, before she became Oracle.
Before Arkham City, the Joker shot her, through the spine. This paralyzed her from the waist down, forcing her into retirement.
In Batman: Arkham Knight, Robin has a thing for Oracle. It was my impression that they were dating.
At the very least, Batman mentions that he won't tell Robin about Oracle, when she is kidnapped and apparently commits suicide, due to "how he feels about her".