Cook the tortellini according to the package directions.
Meanwhile, cook the bacon in a large skillet over medium heat until crisp, 7 to 8 minutes. Reserve the bacon and discard the drippings.
Wipe out the skillet and return it to medium heat. Add the butter and swirl or stir with a wooden spoon as it starts to foam and sputter. Remove from heat as soon as it begins to turn golden brown and smells nutty, about 1 minute.
Break the bacon into small pieces and add to the skillet with the arugula, salt, pepper, and cooked tortellini; toss well. Divide among individual bowls.