Become a Vampire in D&D? Which one makes sence to you?

Actually, you've missed one key element in both of those scenarios. In modern legend, a vampire has to share his blood with his victim in order to turn him. A simple bite won't make a vampire. If it did, every one of the vamp's victims would become a vamp as well, and there goes his food supply. But the second scenario with death makes the most sense, as long as you include the exchange of blood from the vampire as well. That's where you get the transfer of the vampiric "virus".