Edward cannot read Bella's mind because she has a unique supernatural mental shield that blocks his mind-reading abilities. In the Twilight universe, each vampire has a special power—in Edward's case, mind reading. However, Bella possesses a dormant vampire power even while still human, which acts as a mental shield that prevents psychic invasions such as Edward's mind reading. This shield makes her mind private and inaccessible to Edward and others who have similar powers until she becomes a vampire herself. After Bella is turned into a vampire, her ability to control and extend this shield evolves, and she eventually allows Edward to access her mind with her consent. In summary:

• Bella's mind is shielded from Edward's mind-reading power by a unique mental shield she naturally possesses.
• This shield is a dormant vampire ability existing in her even before becoming a vampire.
• Edward can only read her mind after she becomes a vampire and consciously lowers the shield.

This explanation is consistent with the Twilight saga lore and is confirmed in various sources including official Stephenie Meyer material and fan explanations.