In a small bowl, sift together flour, baking powder, baking soda, salt and vanilla pudding mix. In a large mixing bowl, beat sugar and shortening until light, scraping sides of the bowl often. Add the eggs one at a time, beating smooth after each addition. Mix in the milk.
Add flour mixture and mashed bananas alternately to creamed mixture, beating until smooth after each addition. Fold in nuts if desired. Pour batter into a lightly greased 8×4 inch loaf pan.
Bake in a cold, (non-preheated) oven set to 350 degrees F (175 degrees C). Bake for 50 minutes, then cover with foil to prevent burning and bake for additional 10 to 20 minutes or until toothpick inserted into the crown comes out clean. Leave in pan for 10 minutes, then remove from pan and cool.