1. With a paring knife, slice into the pulp of your lime wedge, being careful not to slice through the skin. Use the cut in the lime wedge to evenly wet the entire rim of a rocks glass with its juice.
2. Dip the wet rim of your rocks glass into the lime sugar. Shake off excess.
3. Carefully pour the blackberry shrub, lime juice and orange bitters into your rocks glass. Fill the glass with ice, then top with club soda.
4. Stir gently, and enjoy.