For the peach simple syrup, peel, pit and slice the peaches. Transfer the peaches to a bowl and add the sugar. Toss to coat and set aside for one hour. Set a strainer over a bowl and pour the peaches into the strainer - to collect the peach simple syrup. Leftover peaches can be used in a fruit crisp or as a topping to ice cream or pound cake or in a homemade peach pie.
Add the bourbon, simple syrup, lemon juice and bitters to a cocktail shaker. Add ice and shake vigorously until the cocktail is very cold and frothy, about 30 seconds. Pour into a cocktail glass and serve with a fresh peach wedge, slice of lemon and a maraschino cherry.