On a small plate, combine the sugar and lime zest. Rub the lime wedge around the rim of the glass. Roll and gently stamp the glass in the sugar and lime to coat.
Add the blackberries, lime juice and honey to a cocktail shaker, or jar with a lid.
Using a muddler, muddle the ingredients together, squishing the blackberries so they release their juice.
Add the bourbon and ice. Shake.
Add ice to the rimmed glass. Strain the cocktail mixture over the ice.
Top with bubbly water and stir gently.
Garnish with a lime wedge and serve.
Notes
Use fresh or frozen blackberries. If frozen let the berries thaw on the counter for half and hour.