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.
In the Twilight Series, the author never says that Bella isn't affected by any of the Vampire's gifts. Edward can't read her mind. Alice could see the future and Edward is connected to Bella so Alice can see things that involve Bela. The fact that Edward can't read Bella's mind is not indicative of how she is affected by other vampires. James can track her because her scent is so strong for him. Jasper can relax her and Alice can see the future. The only time we read anything about her not being touched by the gifts is Edward's gift.
The reason why is explained within the books- bella is a shield, but only her mind is protected. Jane only creates the illusion of pain, zafrina creates illusions too, and edward reads minds. All of these gifts work inside the mind, where bella is safe. Alice can see her future because it is not inside the mind, it is actually things that may happen- nothing to do with bellas head at all. Alice sees the future, not the choices behind them. ANd Jasoer doesnt create the illusion of calm or whichever emotion he chooses- he actually does calm the body and mind.
Bella has a power that is like a shield that can protect her from anyone entering her thoughts and she can expand it to protect her family. Jasper can find her scent fast and Alice can see if she will do anything harmful to herself in the future.
because bellas power as a vampire they think is a sheild or something
In the last book Bellas vampiric power is a shield. (as said in the last fight between the top vamps and the cullens) She is not effected by powers that effect her physically but she is affected by thing that deal with her indirectly.
Because alice and jasper dont do things inside of the body
Bella is only not affected by mental powers but she is affected by physical powers. Edward can not read her mind because that is a mental power. Alice can see her in ther visions because she can see where she will be physically. Jasper can affect her emotions because it is affecting her body not just her mind.