Place peppers and onions in center of large sheet heavy-duty foil; drizzle with 1/4 cup steak sauce. Fold to make packet. Grill 2 min.
Meanwhile, mix meat and 2 Tbsp. of the remaining steak sauce; shape into 4 (1/2-inch) patties. Grill 8 to 10 min. or until vegetables are crisp-tender and burgers are done (160F), turning burgers after 4 min. and brushing with remaining steak sauce.
Remove packet from grill; cut slits in foil to release steam before opening packet. Fill rolls with burgers and vegetables.