Preheat oven to 350°F (175°C). Grease a baking pan.
In a mixing bowl, combine gluten-free flour, sugar, baking powder, baking soda, and salt.
Add mashed bananas, melted butter, eggs, and vanilla extract. Mix until well combined.
Pour batter into the prepared baking pan. Bake for 30 minutes or until a toothpick comes out clean. Let it cool.
Cut the cooled banana cake into cubes.
In a trifle dish, layer cake cubes, whipped cream, vanilla pudding, and sliced bananas. Repeat layers until the dish is full.
Chill in the refrigerator for at least 2 hours before serving.