Microwave bacon on paper towel-lined microwave-safe plate for 30 seconds. Crumble.
Blanch rapini in a large pot of lightly salted boiling water for 1 minute. Remove with a slotted spoon; scoop out 1/4 cup water. Return remaining water to boiling; add pasta. Cook 10 minutes, as per package instructions. Drain.
While pasta cooks, heat olive oil over medium heat. Add garlic, olives, red pepper and mushrooms to pan. Cook 3 minutes, until garlic is softened. Add reserved water and rapini. Cook 2 minutes. Toss with pasta, bacon and Parmesan.