Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper.
In a heavy-bottomed skillet over medium-high heat, cook the bacon until crisp and brown. Transfer to paper towels and drain. Chop and set aside.
Whisk the flour, sugar, baking powder, salt, and baking soda in a large mixing bowl.
Using a food processor, pastry cutter, or fingertips incorporate the chilled butter into the dry ingredients until the mixture resembles coarse meal. Add the Cheddar cheese, fresh chives, and cooked bacon. Mix to distribute the ingredients evenly.
Add the buttermilk and stir just until moistened. Using 1/2 cup dough for each biscuit and using a cup measure or an ice cream scoop, drop the biscuits onto the prepared baking sheet, spacing the mounds about 2-inches apart.
Bake until the biscuits are golden brown on top, about 15 to 20 minutes or until a tester comes out clean. Serve the biscuits warm with melted butter.