Technically Babs and Dick were never THAT together in the DCAU.
They started with a not terribly friendly relationship at college (Though Babs was more hostile than Dick was), and ended up dating a couple of times (in Sub-Zero for example) but neither knew about the other's costumed identity and it apparently no further
The events of "Old Wounds" pretty much destroyed the chances of a relationship, and when he came back as Nightwing they never seemed to be more than colleagues. They went to the Iceberg Lounge together in "Joker's Millions" but only to spy on the Joker.
Have to say that the Babs/Bruce pairing will NEVER sit right with me as a concept, nor the undue focus on Batgirl/Batman as a dynamic duo in the last season pretty much completely overshadowing Tim and Dick.