Combine all-purpose flour, whole wheat flour, undissolved yeast, and salt in a large bowl. Heat water, honey and butter until very warm (120° to 130°F). Stir in wheat bran; let stand about 2 minutes. Gradually stir into flour mixture. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Stir in banana and walnuts.Spoon about 1/3 cup of batter into 12 (2-1/2-inch) greased muffin cups. Sprinkle with additional walnuts, if desired. Cover; let rise in warm, draft-free place for about 45 minutes.
Bake at 350°F for 30 minutes or until done. Remove from cups; serve warm.