Preheat oven to 400 degrees F (200 degrees C). Grease a loaf pan with cooking spray.
Mix whole wheat flour, all-purpose flour, oat bran, wheat bran, wheat germ, and baking soda together in a large bowl.
Whisk egg lightly in a small bowl. Whisk in buttermilk. Pour over flour mixture; fold together with a large spoon until batter is moist.
Pour batter into the loaf pan and smooth out the top. Use the spoon to trace a "plus" sign from edge to edge across the top.
Bake in the preheated oven until golden, about 40 minutes. Reduce oven temperature to 225 degrees F (105 degrees C); continue baking until a knife inserted into the center comes out clean, about 25 minutes more.
Invert bread onto a wire rack. Let cool completely, about 1 hour.