Preheat the oven to 350 degrees F (175 degrees C). Grease a 1 1/2-quart baking dish.

Heat a skillet over medium-high heat. Fry bologna slices in the hot skillet until browned on both sides, about 1 minute per side. Drain on a paper towel-lined plate. Wipe excess grease from the skillet, reduce heat to medium, and stir in butter and onion. Cook and stir until onion has softened and turned translucent, about 5 minutes. Stir onion into the warm mashed potatoes.

Spread half of the mashed potatoes into the prepared baking dish. Layer with half of the fried bologna, and sprinkle with half of the cheese. Repeat with the remaining ingredients.

Bake uncovered in the preheated oven until the cheese is bubbly, and the center is hot, about 30 minutes.