In a small saucepan over medium heat, add the honey, lemon juice and water and stir to dissolve. Bring to a simmer and remove from the heat. Set aside to cool slightly (or put it into a shallow pan), then cool completely in the freezer, 30 minutes to 1 hour (but you can leave it longer because it's ok if it freezes).
When the syrup is cold, add 1 cup to a blender with 12 ounces (1 1/2 cups) Bourbon and 1 bunch mint. Add 2 to 4 cups of ice, depending on how strong and thick you want the slushies. Blend until the mixture is thick and frozen like a smoothie.
Divide among 8 small glasses (or 4 tall) and garnish with lemon slices and a sprig of mint. Repeat the process in 3 more batches with remaining ingredients.