Cook the bacon in a medium skillet over medium heat, stirring occasionally, until browned and crisp, about 7 minutes. Transfer to a paper towel-lined plate to drain.
Melt the butter in a medium saucepan over medium heat. Whisk in the flour and garlic; cook, stirring, until incorporated, about 2 minutes. Whisk in the cider, pumpkin puree, mustard, Worcestershire sauce, 1/2 teaspoon salt, the pie spice and cayenne until smooth. Bring to a simmer and cook, stirring occasionally, until thickened, about 3 minutes.
Gradually whisk in the cream cheese and cheddar until melted and smooth, about 2 minutes. Transfer the dip to a bowl; top with the bacon and chives.