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.
Amazingly...yes, she can control herself. The Cullens had prepared for the worst. In Eclipse, we learned just how vicious new born vampires can be when Victoria attempted to use them to kill Bella and the Cullens. They are literally bloodthirsty. So, when Bella completes her transformation and is able to contain herself around Renesmee and Charlie, everyone is plesantly surprised. No one is exactly sure why this is until Bella's power as a shield are revealed. Bella takes to vampirism like a fish to water. Seeing as how her sheilding powers manifested even before she was turned. The family concludes that Bella was "born" to be a vampire. The lifestyle suits her.
Bella still has other new born side effects. She can still smell human blood, however, she has the ability to resist attacking, which is uncommon for newborns. Her eyes are still blood red (due to the leftover human blood in her veins) and her transformation was just as painful as the others. But, for the most part, her first few days and weeks as a vampire go smoothly.
Bella is better than most because she can control her thirst very very well and Edward thinks because she has been around them and heard of their stories and control she was much more controlled. Her powers are also more explained once she becomes a vampire.
In Breaking Dawn Bella is seen unlike any Vampire. Many expected her to be a raving vampire without much control however she is the exact opposite. When coming into contact with the scent of human blood, while she was in her hunting state of mind, instead of charging head first like a new born she held her breath and ran the other way. Then there's her animal diet that she's keen on that surprises many for a newborn vampire. Edward speculates it's from the many stories that the Cullen's have been sharing with Bella that got her ready for the experience.
Bella actually controls the "burning thirst" she feels when she becomes a vampire. A good example is when she is hunting in the forest for the first time. She smells humans and instead of falling into the bloodlust she runs to the cullen home