Preheat oven to 475°. Line a rimmed baking sheet with parchment paper.

In a medium skillet, cook bacon over medium heat until crisp. Remove bacon using a slotted spoon, and let drain on paper towels.

Place flatbreads on prepared pan. Brush with oil, and sprinkle with one-third of Cheddar. Top with half of apple slices, half of bacon, and half of blue cheese. Repeat layers once, and top with remaining one-third of Cheddar.

Bake until golden brown, about 20 minutes.