Bring a large pot of lightly salted water to a boil. Add farfalle pasta, and cook until tender, about 8 minutes. Drain. Place a separate pan of water on to boil. Add asparagus, and cook until tender and bright green, about 3 minutes depending on thickness. Drain, and place into ice water to stop the cooking process.
Heat the olive oil in a large skillet over medium-high heat. Add the onion and bell pepper; cook and stir for about 5 minutes. Add the mushrooms and crawfish tails; cook and stir for another 10 minutes. Add the asparagus and grape tomatoes to the pan, and cook for a couple of minutes. Remove from the heat and transfer to a large serving bowl.
Mix pasta into the serving bowl along with the vinaigrette dressing. Serve immediately, or refrigerate and serve chilled.