1. Cook bacon in large skillet over medium heat until crisp, about 6 minutes. Transfer bacon to paper towel–lined plate. Pour off fat, reserving 3 tablespoons.
2. Pat pork dry with paper towels and season with salt and pepper. Cook pork in 2 tablespoons bacon fat over medium-high heat until well browned all over and meat registers 145 degrees, about 10 minutes. Transfer to platter and tent with foil.
3. Add remaining fat and garlic to now-empty skillet and cook over medium heat until fragrant, about 30 seconds. Stir in half of greens and cook, covered, until greens are beginning to wilt, about 1 minute. Add remaining greens and cook until tender, about 5 minutes. Stir in bacon and 2 teaspoons vinegar. Season with salt and pepper and transfer to plate.
4. Add bourbon, brown sugar, and accumulated pork juices to now-empty skillet and cook until thickened, 2 to 3 minutes. Off heat, whisk in butter, mustard, and remaining vinegar. Pour sauce over pork. Serve with greens.