Cut the chicken breast into small pieces, approximately 2 inches long. Add to a food processor and process until finely ground, about 20 seconds. Stir in bacon, scallions, ginger, mustard, and soy sauce.
Place one dumpling wrapper in the palm of your hand. Scoop a teaspoon of chicken onto the center of the wrapper. Using your other hand, dampen the outer edge of half the wrapper with a little water. Fold the wrapper over the filling and press to seal. (If you want, you can fold little pleats into the seam.) Repeat with remaining wrappers.
Heat the oil in a large skillet set over medium heat. When the oil is hot, add the potstickers, seam-side up. Cook 1 minute, or until the bottom is golden brown. Pour in the water. Cover and cook 3 minutes. Remove cover and cook until water evaporates, about 2 minutes. Gently remove from pan.
Prepare the dipping sauce by whisking together dumpling sauce, chili garlic sauce, mustard, and sesame oil.