Arrange the bread cubes in a single layer on a baking sheet. Bake for 20 minutes or until lightly toasted. Transfer bread cubes into a large mixing bowl. Set aside.
Melt the butter in a large nonstick skillet over medium-high heat. Add the onion and mushrooms to the skillet. Saute for 10 minutes, or until liquid evaporates and vegetables are tender.
Transfer the mushroom and onion mixture to the bread. Toss to combine. Arrange half of the bread mixture in a 13 x 9-inch baking dish coated with cooking spray.
Sprinkle half of the cheese and half of the bacon over top of first layer. Top with remaining bread mixture, cheese, and bacon. In a large mixing bowl, whisk together the milk, eggs, thyme, salt, and pepper until thoroughly combined. Pour the milk mixture over the bread mixture. Cover and refrigerate 8 hours.
Preheat the oven to 350 degrees. Remove the strata from refrigerator and let stand at room temperature for 15 minutes. Bake the strata, covered, 30 minutes. Uncover and bake an additional 15 minutes or until set. Let stand for 10 minutes before serving.