Mix together 1 cup of water, sugar and mint leaves in a small saucepan. Set over high heat and bring to a boil. Cook, stirring until the sugar dissolves, about 5 minutes. Remove from heat and allow the syrup to cool, about 10 minutes.
Pour the syrup through a fine mesh sieve, into a glass jar. Discard mint leaves.
Make Mint Juleps: Fill 4 tin cups with crushed ice. Pour 4 ounces bourbon and 1½ ounces mint syrup into each cup. Gently stir, enjoy.