This one is easy to call. Of course Batgirl Cass loses to the Hulk, but after a year or two of experience and further training, Black Bat Cass easily takes down the Jade Giant. It happens like this...
Okay, okay. That was silly. Almost as silly as imagining a fight between Cassandra Cain and the Incredible Hulk in the first place. It wouldn't really matter which version of Cass fight the Hulk, the Hulk would win. The Hulk defeats most heroes and villains because he's fast, gets stronger the angrier you make him (you know, by doing things like... oh... fighting him), he's indefatigable and close to invulnerable. The Hulk is a Superman-level opponent. He's thumped the Thing on several occasions, after all. Cass has no business fighting the Hulk.
I do remember a comic where Batman tangled with the Hulk and slapped his ears, causing the Hulk to release him from a crushing bear hug. A writer taking liberties. First of all, the Hulk could literally squish Batman between his hands and second of all, I seriously doubt Batman has the physical strength to pop the Hulk's ears. So I don't see Cass faring any better if the Hulk should somehow turn up in Gotham City. What she would do is try to distract him and delay him long enough for the Justice League and the Avengers to come to the rescue. The Hulk and the super-teams would destroy large portions of central Gotham in the ensuing battle, which Cass, Spoiler and the Robins would largely serve as observers of, while rescuing what citizens they could.
After the Hulk reverts back to Bruce Banner and S.H.I.E.L.D. takes him away (Project Cadmus wants him for DNA testing, but Banner falls under the Marvel jurisdiction), Batman grudgingly tells Cass she did a good job, but only after Barbara Gordon shames him into doing so.