Place shrimp and balsamic dressing into a large resealable plastic bag; refrigerate for 15 minutes. Soak toothpicks in water while shrimp is marinating.
Microwave bacon for 1 minute on high. Cut slices in half crosswise (for a total of 24 pieces) and let cool.
Heat broiler. Coat a large broiler pan with nonstick cooking spray.
Remove shrimp from marinade, reserving marinade. Put one piece of bacon on work surface. Place a shrimp at one end; tuck a jalapeño slice into curl of shrimp. Roll bacon up tightly to enclose filling, securing with toothpick. Repeat using all bacon, shrimp and jalapeno.
Stir together mayonnaise, chili sauce, pickle relish, red pepper and 1 tablespoon water. Cover dipping sauce; refrigerate until ready to use.
Place rolls on prepared pan and brush with reserved marinade. Broil 3 minutes. Turn and brush with marinade; broil an additional 2 minutes. Serve with sauce.