Pre-heat oven to 350 degrees Fahrenheit.
In a large mixing bowl, mix together the eggs, milk, sugar, rum, cinnamon and nutmeg.
In a 2 quart baking dish, layer the broken up bread with the mashed banana and blueberries.
Pour milk mixture over the bread and gently press down, allowing the bread to soak up the milk mixture.
Cover with foil and bake for 45minutes. Take foil off and bake for another 10 minutes until top gets slightly golden brown.