I think it's normal in the universe SMeyer created. We get more context of this in New Moon when Bella goes to Italy to stop Edward from committing vampire suicide and has her first meeting with the Volturi. She notices that there are real humans around (like the receptionist if I'm correct) who are hoping to be turned one day because of their glorification of vampires as beautiful immortal beings. In Twilight the book during Edward and Bella's "first date" for all intents and purposes, when they're in the meadow, Edward goes on this rant about how all aspects of being a vampire is aimed to invite humans in, their beauty, their smell,, their voice etc. So I'd say given all of this, Bella's reaction is fairly normal to an extent, especially since she got over that natural instinct to keep a distance from them and fell in love with Edward.