Preheat grill or smoker. Preheat grill or smoker to 250-275℉ with your choice of wood or pellets.
Par-cook the bacon slices. Cook bacon slices until slightly less than halfway cooked through, about 3-4 minutes. Be careful to not cook the bacon until done - you want it to be very pliable still to wrap the dove breasts. Cool the par-cooked bacon on paper towels to drain excess grease.
Wrap the dove breasts in bacon. Lay one piece of partially cooked bacon flat on a cutting board. Place one dove breast at the end of the bacon, and roll up, wrapping the bacon around the breast. Secure the end with a toothpick. Repeat for all dove breasts.
Season the dove breasts. Lightly season each bacon wrapped dove breast with BBQ seasoning. As you finish seasoning the breasts, place them on a wire cooling rack with about 1 inch in between each piece.
Cook dove breasts on the grill. Place the wire cooling rack with the dove breasts directly on the grill grates, close the grill lid, and smoke until the bacon is cooked through and the internal temperature of the dove breast is about 160-165℉, about 1 hour. *Cooking times may vary based on the temperature of your grill, etc.
Make the sauce. When the doves have about 10-15 minutes left on the smoker, make the sauce. In a small saucepan over medium heat, whisk together barbecue sauce, grape jelly, and chili sauce. Continue to cook, stirring occasionally, until the ingredients are evenly combined and the sauce has reduced just a bit, about 5-6 minutes. Then add the sauce to a large mixing bowl. Set aside. *You may need to reheat the sauce to thin it out a bit before saucing the smoked dove breasts.
Sauce the dove breasts. When the smoked dove breasts are done on the grill, transfer them to the bowl with the sauce. Gently stir so that the doves are evenly coated in the sauce. Serve immediately.