Preheat the oven to 375 degrees F (190 degrees C). Grease and flour a 9x13-inch baking pan.

Mix sugar, sour cream, butter, and eggs in a large bowl using an electric mixer on low speed for 2 to 3 minutes. Scrape bowl and add bananas, vanilla extract, and rum flavoring; beat well.

Combine flour, salt, baking soda, cinnamon, ginger, and nutmeg in a bowl; mix well. Stir flour mixture into banana mixture and beat on medium speed until well mixed, 1 to 2 minutes. Fold in chocolate chips. Spread batter into the prepared pan.

Bake in the preheated oven until a toothpick inserted in the center comes out clean, 20 to 25 minutes. Cool completely before cutting into bars.