Cut the mozzarella into 12 short, thick pieces approximately 3/4 inch wide and 1 to 1 1/4 inches long. Avoid very thin pieces because they will melt faster.
Arrange the mozzarella pieces on a small plate or tray and freeze for 45–60 minutes. The cheese should be very cold and firm before wrapping.
Preheat the grill, pellet grill, or smoker to 375°F. If using charcoal or gas, establish an indirect cooking zone so the bacon will not sit directly above an open flame.
Place a wire rack over a rimmed sheet pan or other grill-safe pan. The pan will catch rendered bacon fat and any cheese that escapes.
Cut each strip of bacon in half crosswise to create 12 shorter strips.
Remove only a few pieces of mozzarella from the freezer at a time so the remaining cheese stays as cold as possible.
Wrap one bacon strip tightly around each mozzarella piece. Position the bacon so it overlaps itself and covers as much exposed cheese as possible.
Secure the overlapping bacon with a toothpick and place each bite seam-side down on the wire rack.
Lightly season the outside of the bacon with BBQ rub. Do not heavily coat the bites because the bacon, cheese, rub, and sauce all contribute salt.
Place the pan over indirect heat and cook for approximately 18–23 minutes, or until the bacon has rendered, browned, and is approaching crisp. Watch for signs that the mozzarella is beginning to soften or escape.
While the bites cook, combine the BBQ sauce, maple syrup, and apple cider vinegar in a small bowl.
Once the bacon is nearly cooked, lightly brush each bite with the BBQ glaze.
Continue cooking for approximately 3–5 minutes, just until the glaze becomes tacky and lightly caramelized and the bacon is fully cooked.
Remove the bites from the cooker immediately once the bacon is finished. Avoid unnecessarily extending the cooking time because the mozzarella will continue to soften.
Let the bites rest for approximately 5 minutes before serving. The cheese inside will be extremely hot.
Remove the toothpicks before serving, or make sure guests know they are present.