This is the kind of thing that I think about at night.
How would it effect the Hulk? Would the Hulk become even more awesomely powerful with the addition of vampire powers? Would the Hulk still have the same weaknesses as any normal vampire, or could he cancel them out?

the same thing that Would happen if he was bitten by a Wendigo, we would just get another new Random Hulk

but would his tagline be "HULK SUCK!" ?

Can never happen since there aren't teeth strong enough to penetrate Hulk's skin. Hulk fought a werewolf once and he claimed that "if he bites me, he'll break all his teeth"... and i guess that's what would happen.

But the question was what if a vampire bit Banner? Not Hulk. I think he'd prolly change before the vampire had a chance to bite him. But if he didn't, I'm guessing the gamma in Bruce's blood would effect the vampire more then the bite would effect Banner. IDK just guessin here.

He has gained large immunity of many earthly sicknesses for sure.