Toss cubed bread with bacon, cheese, and mushrooms, and pour into a 9x13 inch baking dish. Whisk together eggs, half-and-half, and mustard until smooth, then pour evenly over cubed bread. Cover dish with plastic wrap, and refrigerate overnight.
Preheat oven to 350 degrees F (175 degrees C).
Remove plastic wrap from the baking dish, and bake strata in preheated oven until the top is golden brown, and the eggs are set, about 1 hour. Let stand for 10 minutes before serving.