In a small saucepan, combine the first 9 ingredients. Bring to a boil. Reduce heat; simmer, covered, until thickened, 5-8 minutes. Reserve 1/4 cup sauce for wraps.
Moisten a paper towel with cooking oil; using long-handled tongs, rub on grill rack to coat lightly. Sprinkle chicken with salt and pepper; place on grill rack. Grill, covered, over medium heat 7-8 minutes. Turn; grill until a thermometer reads 165°, 7-8 minutes longer, brushing occasionally with sauce. Top with cheese; grill, covered, until cheese is melted, 1-2 minutes longer. Let stand 5 minutes before slicing into strips.
Spread dressing over tortillas. Top with chicken; drizzle with reserved sauce. Top with bacon and if desired, lettuce. Fold bottom of tortilla over filling; fold both sides to close.