The answer to this question is revealed in Breaking Dawn. Once Bella has become a vampire, we learn that she is a shield. Not only can she block the mental gifts of others, but she eventually learns how to spread her gift to protect others. Bella is impervious to gifts that effect her mind like the gifts of Edward and Jane. Edward can hear the thoughts of anyone except for Bella. It is one of the things that initially intrigues him about her. Similarly, Jane (the Volturi's favorite) tries as hard as she can to hurt Bella with her gift, but Bella does not flinch. Alice and Jasper's gifts still affect her because they affect her outwardly. Alice does not need to see into Bella's mind to see the future. Similarly, Jasper has the ability to create particular atmospheres. He isn't calming the actual person, it's in the atmosphere, which explains why everyone in the room feels it and why when he leaves, the atmosphere changes.