Chill your glasses while the tea mixture chills. You can also shake the cocktail with ice before serving, but strain the ice before you pour.
Combine sugar and 1/2 cup water in a microwave-safe bowl; microwave at high 3 minutes, stirring until sugar dissolves. Add tea bags and mint to sugar syrup; steep 20 minutes. Discard tea bags and mint. Stir in bourbon and juice; chill. Pour tea mixture into a pitcher; stir in sparkling wine. Garnish with mint sprigs, if desired; serve immediately.