Preheat oven to 350 degrees F (175 degrees C). Lightly grease and flour a fluted tube pan (such as a Bundt®.

Combine flour, baking soda, baking powder, and salt in a bowl.

Place butter and sugar in a blender; process until sugar is almost completely dissolved; pour into a bowl. Stir in mashed bananas and egg until well blended; pour banana mixture into flour mixture and stir until batter is just combined. Pour batter into prepared tube pan.

Bake in the preheated oven until a knife inserted into the center comes out clean, 30 to 35 minutes. Cool in the pan for 10 minutes before inverting cake onto a plate to serve.