Preheat oven to 350º F. Line muffin pan with paper liners and set aside. Whisk together flour, baking powder, baking soda, and salt and set aside. Toss blueberries to coat them well in 1 tablespoon of all-purpose flour and set aside.
Cream together bananas and granulated sugar until well-combined with an electric mixer, about 2 to 3 minutes. Then, incorporate butter, egg and vanilla. Fold flour mixture into banana mixture until well combined and then carefully fold in coated blueberries. Scoop batter into prepared muffin pans, filling them about 3/4 full.
Bake until golden and muffins spring back to the touch, about 25 minutes. Additionally, a toothpick should come out clean when inserted into the center of a muffin. Allow to cool slightly before removing from muffin pan.