Fry bacon in an ovenproof skillet until it is crisp; drain and crumble it. Saute onion and green pepper in the bacon fat until tender (not browned).
In a medium bowl combine chicken, mayonnaise, bacon crumbles, onion and green pepper, 1/4 teaspoon onion powder, 1/4 teaspoon garlic powder, 1/4 teaspoon salt and cayenne pepper. Set aside.
Remove stems from the mushroom caps. Clean them by rubbing them with a paper towel and pulling the skin off that is by the gills. If you prefer, they can be skinned or peeled.
Melt 2 tablespoons butter in the same pan. Place mushroom caps into the skillet gill side up and lightly brown. Sprinkle with remaining onion powder, garlic powder and salt. Flip the mushroom caps and cook for another 2 or 3 minutes.
Turn the caps so they are gill side up again. Equally divide the chicken mixture among the caps, placing it in the center of each cap. Flatten it down slightly to fit the cap. Top each with 1 tablespoon grated cheddar cheese. Bake in a 350 preheated oven for 15 minutes. Be careful not to burn the cheese.
Remove from the oven and place on a serving platter. Garnish as desired.