Cook linguine. Drain, reserving 1 1/2 cups pasta water; return pasta to pot.
Meanwhile, cook sausage and 2 tablespoons water in a large covered nonstick skillet over medium until fat renders, 5 minutes. Uncover; raise heat to medium-high. Brown sausage, breaking it up with a spoon, 7 minutes.
Add garlic, bell peppers, and 1/4 cup reserved pasta water; cook until peppers soften, 6 minutes. Add 3/4 cup pasta water and butter; swirl to combine.
Transfer to pot. Add arugula; season with salt and pepper. Toss; add more pasta water as desired. Serve.