Place bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain bacon strips on paper towels, reserving 1 tablespoon of grease in the skillet. Chop bacon into large chunks.
Saute onion and mushrooms over medium-high heat in the same skillet until golden brown, about 8 minutes. Add wine and reduce heat to medium, stirring frequently, until wine reduces by half, about 5 minutes. Remove onion mixture from heat.
Preheat an outdoor grill for medium heat and lightly oil the grate. Place hamburger buns on grill until lightly toasted, 2 to 3 minutes.
Shape ground beef into 8 patties. Sprinkle salt, garlic powder, and ground black pepper over patties.
Cook patties on the preheated grill until browned on one side, about 6 minutes. Flip patties, top each with one slice of cheese and continue grilling until no longer pink in the center, about 6 minutes more. An instant-read thermometer inserted into the center should read at least 160 degrees F (71 degrees C).
Transfer burgers to toasted buns. Place some of the onion mixture on top using a slotted spoon. Add chunks of bacon.