Arrange bread in a single layer on a jelly-roll pan. Bake at 350° for 20 minutes or until toasted. Place bread cubes in a large bowl.
Melt butter in a large nonstick skillet over medium-high heat. Add onion and mushrooms to pan; sauté 10 minutes or until liquid evaporates and vegetables are tender. Add onion mixture to bread; toss well to combine. Arrange half of bread mixture in a 13 x 9-inch baking dish coated with cooking spray. Sprinkle with half of cheese and half of bacon; top with remaining bread mixture, cheese, and bacon.
Combine milk and next 4 ingredients (through salt), stirring with a whisk. Pour milk mixture over bread mixture. Cover and refrigerate 8 hours.
Preheat oven to 350°.
Remove strata from refrigerator; let stand at room temperature for 15 minutes. Bake strata, covered, at 350° for 30 minutes. Uncover and bake an additional 15 minutes or until set. Let stand 10 minutes before serving. Garnish with thyme sprigs, if desired.