Adjust oven rack to upper-middle position and heat oven to 400 degrees.
Fry bacon in large nonstick skillet over medium-high heat until crispy, about 4 minutes. Transfer to a large paper towel-lined plate and pour off all but 1 tablespoon fat.
Pat chicken dry with paper towels and season with salt and pepper. Cook chicken in bacon fat until browned on one side, about 4 minutes.
Flip chicken and add barbecue sauce, chile and water. Cover, reduce heat to medium, and simmer until chicken is cooked through and sauce is slightly thickened, about 8 minutes. Remove chicken from skillet and slice crosswise into 1/4-inch pieces.
Arrange buns cut side up on baking sheet. Divide chicken among bottom halves of rolls and top with sauce, cheese, bacon and green onions. Bake open-faced sandwiches in oven until cheese melts and buns are golden brown, about 4 minutes.