For the simple syrup: Combine the sugar and 1 cup water in a small saucepot over medium heat. Bring to a simmer and cook, whisking occasionally, until the sugar dissolves, about 5 minutes. Remove from the heat and cool to room temperature. Refrigerate in an airtight container for up to 2 weeks.
For the pisco sour: Fill a cocktail shaker with the ice, and then pour in the pisco, 3/4 ounce simple syrup, the lemon juice and egg white. Shake very well, and then strain into a tall champagne flute. Garnish with 3 drops of bitters.