Beat butter with an electric mixer until completely smooth and creamy. Gradually add powdered sugar, about 1 cup at a time, beating until sugar is fully incorporated into butter after each addition. Add bourbon in a slow, steady stream, beating well. Transfer to an airtight container, and chill until firm, about 1 hour.
Shape chilled bourbon mixture into 28 balls (about 1 tablespoon each). Drop each one into melted chocolate to coat; remove with a fork, and place on a parchment-paper lined baking sheet. Freeze until firm, at least 2 hours.