Does Esme Cullen have special abilities?

Bella Swan doesn't have any "power".

Though it's not a power exactly, Bella is immune to Edward, Aro, Jane, and Alec's powers.

actually, Bella Cullen DOES have a power. she can stretch her shield of blockage to mind powers. For example, if Jane wanted to give Edward pain, Bella could stretch her power to where Edward is and he wouldn't be able to feel pain.