Combine 2 cups water and sugar in a saucepan over medium heat, stirring until sugar dissolves. Add mint; bring to a boil. Remove from heat; cover and steep 30 minutes. Pour mint syrup through a fine wire-mesh strainer lined with cheesecloth. Let cool.
Combine syrup and bourbon. Pour into a sterilized bottle; cover tightly, and chill at least 1 month. Serve over ice. Garnish, if desired.