It's like she's trying way too hard to seem casual. Because of course that's not what genuinely casual Babs sounds like either. This is the earliest scene I know of where Diana, acting on her own and not as part of a League effort, specifically seeks Oracle out, and one of the earlier instances of someone outside the Batclan doing so, so maybe Babs is just thrown by being relied on.
Or she's trying to be suave and flirty. Always a good option too.