Bella is exceptional as a vampire. Of course, as a new vampire, she experiences the "burning thirst" for human blood that other vampires experience. However, unlike other newborn vampires, Bella can control herself and her urges around human beings. For instance, on her first hunting trip, she accidentally stumbles upon a group of humans. However, instead of attacking them like another newborn vampire would, she fights her instincts and walks away.
Not only is Bella blessed in the ability to control her vampire urges, she is also innately an exceptional hunter, and, unlike her human self, she is stealthy and well-coordinated. It is as if she was born to be a vampire, and even the Volturi agree.