Combine 2 Tbsp. bourbon and 1 1/2 tsp. fresh lime juice in a cocktail shaker; fill with ice. Cover with lid, and shake vigorously until thoroughly chilled (about 30 seconds). Strain into a 10-oz. glass filled with ice. Top with 6 Tbsp. of your favorite ginger ale or ginger beer. Drizzle with 1/4 tsp. grenadine. Garnish with fresh lime slices or wedges.