Combine water and dark brown sugar in a microwave-safe dish; microwave at HIGH 2 minutes, stirring until sugar dissolves. Cool, then chill. Stir chilled fresh lemon juice and bourbon into chilled sugar syrup mixture. Divide mixture evenly among 4 glasses, and top each serving with about 3 tablespoons chilled dry sparkling wine and 2 to 3 dashes bitters. Serve immediately.