Preheat oven to 350 degrees F. Line a 12-cup muffin tin with muffin liners or spray with non-stick cooking spray. Set aside.
In a medium sized bowl, whisk together the gluten-free flours, baking soda, and salt. Set aside.
In a large bowl, whisk the egg. Add the sugar, oil, mashed bananas, applesauce, and vanilla extract. Whisk until well combined.
Add the dry ingredients to the wet ingredients. Stir until just combined. Do not overmix. Gently fold in the blueberries.
Divide the batter evenly among the 12 muffin cups, filling each about two-thirds full.
Bake for 20-25 minutes, or until a wooden skewer inserted into the center of a muffin comes out clean.
Remove from oven and let cool in the muffin tin for 5 minutes before transferring to a wire rack to cool completely.