Combine the sugar and 2 cups water in a saucepan and bring to a simmer over medium heat. Remove from the heat and submerge 3 bunches of mint. Let stand at least 1 hour, or preferably overnight. Strain.
Stir together the mint simple syrup (you should have 2 1/2 cups) and bourbon in a pitcher. Add a couple of sprigs of mint for garnish. Refrigerate until ready to serve, up to 8 hours.
Pack 8 mint julep cups with crushed ice. Pour 4 ounces of the mint julep mixture into each; garnish with a mint sprig and serve with a straw. When the outside of the cup has frosted over, you are ready to enjoy.