Bring a large pot of lightly salted water to a boil. Cook farfalle at a boil, stirring occasionally, until tender yet firm to the bite, about 12 minutes. Drain; rinse with cold water until cool. Transfer to a large bowl; refrigerate until ready to use.

Meanwhile, cook bacon in a large skillet over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain on a paper towel-lined plate. Chop when cool.

Combine dressing, bacon, red onion, carrot, celery, and Parmesan cheese in a large bowl; stir in pasta to coat. Refrigerate to blend flavors, about 2 hours.