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.