1. Move oven rack to low position so that tops of pans will be in center of oven. Heat oven to 350°F. Grease bottoms only of 2 loaf pans, 8 1/2x4 1/2x2 1/2 inches, or 1 loaf pan, 9x5x3 inches.
2. Mix sugar and butter in large bowl. Stir in eggs until well blended. Add bananas, buttermilk and vanilla. Beat until smooth. Stir in flour, baking soda and salt just until moistened. Stir in nuts. Pour into pans.
3. Bake 8-inch loaves about 1 hour, 9-inch loaf about 1 1/4 hours, or until toothpick inserted in center comes out clean. Cool 10 minutes. Loosen sides of loaves from pans; remove from pans and place top side up on wire rack. Cool completely, about 2 hours, before slicing. Wrap tightly and store at room temperature up to 4 days, or refrigerate up to 10 days.