In a small sauce pan over medium heat combine the water, grilled lemon juice, and sugar. Simmer and stir occasionally until the sugar dissolves (about 10 minutes).
Remove from heat and let cool. Store in a mason jar in the refrigerator for up to 10 days.
For the Bourbon Cocktail
In a low ball glass, add ice cubes. Using a cocktail jigger add bourbon and simple syrup to the glass and 3 dashes of the bitters. Stir and enjoy.
Notes
The simple syrup yields 2 cups of grilled lemon simple syrup and should be good for up to 6 total cocktails.