Preheat the oven to 350 degrees F (175 degrees C). Lightly grease an 8x4-inch loaf pan.
Combine sugar, butter, bananas, and eggs in a large mixing bowl. Add in flour, milk, vanilla, baking soda, and salt; beat well. Pour batter into the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center of the loaf comes out clean, about 60 minutes.