In a bowl, dissolve yeast in warm water; set aside. In another bowl, combine boiling water, oil, sugar and salt; stir until sugar is dissolved. Stir in cold water and bran. Stir into yeast mixture. Add whole flour and 1-1/2 cups all-purpose flour. Beat on medium speed for 2-3 minutes. Stir in enough remaining all-purpose flour to make a stiff dough.
Turn onto a floured surface; knead until smooth and elastic, about 8 minutes. Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled, about 1 hour.
Punch the dough down; cover and let rest for 8 minutes. Shape into a loaf. Place in a greased 9x5-in. loaf pan. Cover and let rise until doubled, about 45 minutes. Bake at 350° for 35-45 minutes or until golden brown. Remove from pan to cool on a wire rack.