Position oven rack to center position. Preheat oven to 400 degrees F (200 degrees C). Butter a 10-inch pie plate.
Heat a large skillet over medium heat; cook and stir bacon in the hot skillet until crisp, 5 to 10 minutes. Remove bacon and drain all but 2 tablespoons grease from skillet. Cook and stir asparagus and mushrooms in the remaining bacon grease until asparagus is tender, about 5 minutes.
Remove skillet from heat and toss bacon into asparagus mixture. Spread asparagus-bacon mixture into the prepared pie pan. Sprinkle Swiss cheese over mixture.
Whisk cream, eggs, salt, and pepper in a bowl. Pour egg mixture over asparagus-cheese mixture.
Bake in the preheated oven until quiche is set and a knife inserted in the center comes out clean, about 30 minutes.
