Pulse flour, salt, and sugar in food processor work bowl fitted with steel blade. Scatter butter pieces over flour mixture, tossing to coat with flour. Cut butter into flour with five 1-second pulses. Add shortening and continue cutting in until flour is pale yellow and resembles coarse cornmeal, with butter bits no larger than small peas, about four more 1-second pulses. Turn mixture into medium bowl.
Adjust oven rack to center position and heat oven to 375 degrees. Fry bacon in skillet over medium heat until crisp and brown, about 5 minutes. Transfer with slotted spoon to paper towel-lined plate. Meanwhile, whisk all remaining ingredients except cheese in medium bowl.