Siring a vampire requires more than just a bite. In some stories it's looked at as a disease (Blade) but for the most part that's not correct.
Vampirism is more along the lines of demonic possession. To reproduce, vampires must drain a human being of most of his or her blood and bringing his or her soul just to the point of death, then forcing the human to consume some of the vampire's blood. This can be something as simple as the vampire biting his own wrist and allowing blood to drip into the victims mouth. A demon is summoned to take over your body, which retains your memories and to some extent your personality due to the human soul still being trapped within the body. The demon takes possession of the host body and becomes a vampire.
Vampires usually sire someone in order to spend eternity with them, although in some cases this isn't true. Angelus sired vampires to play head games with Buffy when he lost his soul. Spike was siring vampires against his will when he was being triggered and controlled by The First.
Most often they just kill to feed or torment, so the blood transfer is not initiated.