I think Edward's venom had a great deal to do with how Bella was after she transformed.
My interpretation of La cantua tua (or whatever the term is, exactly) is that it serves the same function as the imprinting of the shapeshifters; that it aligns an ideal 'genetic' match between a vampire and a human in such a way that a bite is inevitable, to procreate the species. But, like everything else vampiric, it's overdone to an extreme, which in most cases makes it counter-productive.
There are a couple comments I base this on, the main one being the repeated remark that Bella seemed 'designed to be a vampire'. I haven't quite the time to hunt down every remark, but I know it was said a couple times before Alice mentions it during the transformation. The Italians also remark that she's one of the most promising humans for a transformation (specifically for her talent). In MS, Edward ponders reasons that Bella had been put in front of him as an irresistable force: her smell, her resistance to his ability, her (curious) lack of fear for him specifically, as though she were designed to be an ideal companion for him.
In a broader sense, Edward and Bella act in many ways similar to an imprinted pair: if not love at first sight, they were definitely entranced with one another from their first glance. And a full 'imprinting' wouldn't make sense 'genetically': attaching wholy to one person to the exclusion of all others wouldn't make much sense to vampiric 'breeding' as it would to shapeshifters.
Bella's clumsiness is another hint. Although it's a defining aspect of her human nature, within moments of her transformation she's described as 'graceful, even for a vampire,' without even practicing. Like a puppy growing into it's too-large paws, I imagine Bella's more suited to another form: her human self is awkward, in a transitional state, not a finished one.
The control she has in her final form is another supporting feature, although minor in my opinion, since other ideas were forwarded to account for it: namely her own shield and her preparation as a human.
I think that, had Bella been changed by any vampire other than Edward, she wouldn't have had such an easy and spectacular transformation.