Preheat oven to 350 degrees. Place bananas in a large bowl and mash with electric mixer. Stir in honey and let stand for 15 minutes.
Add applesauce, vanilla and eggs and beat well. Sift flour, baking powder, baking soda, and salt. Add flour mixture to wet ingredients. Mix thoroughly. Coat 9" X %" loaf pan with nonstick vegetable spray and pour in mixture. Bake for 50 minutes or until a woden toothpick inserted in the center of the loaf comes out clean. Remove from oven and let stand 10 minutes before removing from pan. Cool on wire rack.