Across bottom of lightly greased 9 x 9 x 2-inch baking dish, arrange bread slices, slightly overlapping. Set aside.
In large bowl, beat together eggs, milk, bacon, 2 tablespoons each of Swiss and Cheddar cheeses, mushrooms and salt, if desired. Pour mixture over bread slices. Sprinkle potatoes and remaining cheeses over egg mixture. Cover and refrigerate overnight.
Bake, uncovered, in preheated 350ºF oven until lightly browned and knife inserted near center comes out clean, about 40 to 45 minutes.