That is a very good question. We don't really know why Bella isn't afraid of vampires, or wearwolves for that matter. Bella has a strange way of looking at the world in general. Her mother, according to what we read is a "flake." Her father is the sheriff of a small town called Forks, yet, he is not very strict and Bella has a great deal of freedom to come and go. Bella, as Edward once states, "you are afraid that my family won't like you, but you are not afraid to be going into a house full of vampires."
We can assume that one of the reasons Bella is so accepting of the differences in people is because she wasn’t very popular and never felt as if she fit in. "When her mother remarried, Bella decided to move back to Forks to live with her father. She felt a bit guilty that her mother wasn’t able to spend as much time traveling with her new husband because of her, and so willingly, but not enthusiastically, she moved in with her dad. He bought her a truck and has tried to make her feel comfortable in her new home," but she is not comfortable and still feels very shy and introverted.
Bella attracts danger to herself. She wanted to find out who Edward was and what he was like. What there was about him and even trying to find out more about him and how he is a vampire and sticking with him. She wanted to find out and kept on exploring.
Bella has a curiosity as they say would kill the cat. Edward once said that she was magnet for trouble. Edward even laughed at her when he was going to take her to go see his family for the first time. Bella was not worried about the fact that she was about to intrude on a house of vampires but rather if they would like her or not. I think Bella has just accepted that she's with the in crowd of unnatural people and goes with the flow haha.
Because in her destiny she was suposed to become a vampire and she waws in love with edward
In Eclipse, Stephanie Meyer attempts to address this very questions. She talks about how Bella is different and is not affected like others. She has "a very private mind." Her mind is so private that Edward is not able to hear her thougths. Meyer addresses this on her website as well.
in stephanies partial draft of midnight sun edward thinks that she was sent as a gift to him and the fact that he cant hear her thoughts grabs his attention her beauty keeps him intrested and her horrible bad luck gives him a reason to stay. she was sent to him and therefore not afraid she was meant for that world