Prepare a 9x13 casserole dish with nonstick cooking spray. Place cut up bagels in an even layer across the bottom of the casserole dish. In a mixing bowl, beat the eggs, milk, salt, vanilla, and bananas until well blended.
Pour the egg mixture over the top of the bagel pieces. Cover the casserole dish with foil and refrigerate overnight (or for at least 2 hours.)
When ready to cook, remove the casserole from the refrigerator and allow it to rest on the stove top as the oven preheats to 350 degrees.
Bake uncovered for 45 to 50 minutes or until a knife inserted in the center returns clean. Allow to rest for 10 minutes prior to serving.