Preheat the oven to 400°F / 205°C. Grease a non-stick muffin tin, or line a muffin tin with quality paper. See the tips in the post about preventing this low fat muffin from sticking to the paper.
In a large bowl, whisk together the wheat bran, flour, baking powder, salt, cinnamon, and ginger.
In a medium bowl, beat together the sugars and eggs using a hand mixer on low speed for about 30 seconds, until everything is mixed. Add in the milk and vanilla extract and beat for 10 seconds on low speed. Add in the mashed bananas and apple sauce, and beat for another 10 seconds until everything is all mixed.
Make a well in the dry ingredients and pour in the banana mixture. Using a spatula, fold the ingredients together until the batter is just mixed, being careful not to over mix the batter. Set aside and let stand for 5 minutes.
In the meantime, wash and dry the blueberries. Toss the blueberries in the flour so they are lightly coated.
Gently fold the blueberries into the batter, reserving a 12-24 blueberries to place on top of the muffins if you desire.
Evenly divide the batter into the muffin cups. Place the reserved blueberries on top of the muffins, pushing them in so only the tops of the blueberries are not tucked in the batter.
Bake for 10 minutes. Reduce the heat to 350°F / 176°C. Bake another 25 minutes or so, until a toothpick inserted into the muffins come out clean.