Preheat oven to 350 degrees.
Combine the flour, baking soda and salt in a small bowl.
In a large bowl, cream together the butter and sugars. Add the eggs, vanilla, and pudding mix, and mix well.
Add the flour mixture to the large bowl, and stir until combined.
Stir in chocolate chips and 1/2 of the chopped Butterfinger bits.
Put the mixture into a 9x13 baking pan, and top with the remaining Butterfinger bits.
Bake for approximately 20 minutes or until a toothpick inserted in the center of the bars comes out clean.
Cool for 30 minutes before slicing and serving.