Working in batches, cook the bacon in a 12-inch skillet over medium heat until crisp, about 8 minutes per batch. Transfer to a paper-towel-lined plate and drain off all but 1 Tbs. of the fat. Return the pan to medium heat, add the garlic, and cook until fragrant, about 30 seconds. Stir in the spinach and cook until just wilted, about 30 seconds longer. Season to taste with salt and pepper.
Heat a panini or sandwich press according to the manufacturer’s instructions. (Alternatively, heat a nonstick grill pan over medium-high heat.)
While the press is heating, arrange the spinach on 4 pieces of the bread. Top each with some bacon, mozzarella, and tomato, sprinkle lightly with salt, and complete each sandwich with a slice of the remaining bread. Brush both sides of the sandwiches with the oil.
Put the sandwiches on the press, pull the top down, and cook until browned and crisp and the cheese is melted, 3 to 6 minutes, depending on how hot your machine is. (If using a grill pan, put a heavy pan on top of the sandwiches and cook, turning the sandwiches over once.) Carefully remove from the press and serve.