Place bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain the bacon slices on paper towels, reserving bacon grease in skillet; crumble bacon.
Melt butter in bacon grease over medium heat; cook and stir onion, celery, and garlic until tender and lightly browned, about 15 minutes. Transfer vegetables and bacon to large bowl; stir in mashed potatoes, American cheese, flour, egg, mustard, black pepper, and hot sauce.
Heat vegetable oil in a clean skillet over medium heat. Drop spoonfuls of mashed potato mixture, flattening slightly, and fry patties until golden brown on both sides, 5 to 7 minutes. Serve with sour cream.