In a medium-sized bowl or dish, whisk together the honey, mustard and Italian dressing. Reserve about a half a cup of the dressing for slathering on the toasted buns when ready to serve.
Place the chicken into the marinade are turn until all cutlets are well coated.
Pre-heat oven to 400°F. Place the bacon on 1 (or 2) baking sheets and bake until crisp, about 8 to 10 minutes (time will vary depending on how thick the bacon is). Flipping half way through the baking. Set aside.
Meanwhile, turn your grill to medium-high heat.
Grill the marinated chicken until nicely browned. Sprinkle salt and pepper over the cutlets on each side as they cook. Brush more of the marinade over the cutlets until they are golden brown and the glaze has slightly caramlized. Remove from the gril.
Grill the buns until nicely browned.
On a baking sheet, place 4 chicken cutlets, then criss-cross two slices of cooked bacon, and repeat this. Place cheese slices on top. Turn your broiler on high and then cook just until the cheese has melted, about 1 to 3 minutes. Keep and eye on this...don't let them burn!
Slather a good layer of the reserved honey mustard dressing on the toasted buns. Add mayonnaise, too, if desired. Place the prepared chicken/bacon/cheese on the buns and serve at once.