Preheat the oven to 400. Sprinkle a little salt on the shredded zucchini. Set aside.
In a medium bowl combine the cheeses, bacon, egg, and seasonings. Squeeze as much liquid from the zucchini as possible. Add it to the filling and mix well.
Divide the filling between the mushrooms. Bake for 20-30 minutes until the filling is golden and the mushrooms have softened.