I’ve just started listening to the unabridged audio book version of Dead Until Dark, so I’ll clarify a few things from the book perspective.
When Bill feeds Sookie to heal her, she says she doesn’t want to be a vampire. He tells her it won’t turn her, but doesn’t give any more explanation then. A day (night?) or two later after Bill meets Sookie’s grandma, Sookie asks him how you become a vampire. He says that you need to have all your blood drained in one feeding, or over a couple of nights. You then drink from the vampire. You’ll appear dead for a few days, then wake up “hungry”. Bill also says it’s possible for people who are fed from repeatedly and deeply to become vampires.