►If using refrigerated pizza dough, leave out at room temperature for about an hour before working with it. Meanwhile, heat the grill to medium-high, direct heat between 400°F to 450°F.
►To make the pickled red onions: Stir together water, apple cider vinegar, sugar, and salt in a small bowl until sugar and salt are dissolved. Add onion, pressing down lightly to submerge, and set aside.
►Place bacon in a large skillet over medium-low heat and cook, flipping halfway through, until the fat has rendered out and the bacon is crispy, about 10 minutes total. Transfer bacon to a paper towel-lined plate to drain and cool, about 5 minutes. Once the bacon is cool enough to handle, chop or crumble the strips into small pieces.
►Place pizza dough on a well-floured baking sheet. Use the heel of your hand to press the dough flat. With your hands, work from the middle out to stretch and shape the dough into roughly a 12- by 10-inch rectangle. If dough starts to shrink back, wait a few minutes to let it relax and continue shaping.
►Brush dough with half the olive oil. Lay dough on the grill with the olive oil-side down. Let cook, uncovered, until you see light grill marks on the bottom of the dough when you lift a corner of it with tongs or a spatula, 2 to 3 minutes.
►Brush the top of the dough with the remaining 1 tablespoon olive oil and flip it over. Sprinkle the dough evenly with the bacon and blue cheese crumbles. Cover and cook until the edges of the flatbread are golden-brown and crisp and the cheese has softened and slightly melted, about 3 minutes more.
►Carefully transfer the flatbread to a clean cutting board. Top with arugula and pickled red onion and let cool for 2 or 3 minutes before slicing and serving.