In a small saucepan, combine sugar and ½ cup water. Bring to a boil over medium-high heat. Reduce heat to medium-low; simmer until sugar dissolves, approximately 2 minutes. Remove from heat; let cool slightly.
Pour sugar mixture into a pitcher. Add peaches, bourbon, and bitters. Cover, and refrigerate until chilled, approximately 2 hours. Just before serving, add sparkling water. Serve over ice. Garnish with mint, if desired.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/peach-bourbon-fizz-recipe/