Various embodiments of the invention include turbine buckets and systems employing such buckets. Various particular embodiments include a turbine bucket having: a base including: a casing having at least one exhaust aperture on an outer surface of the casing; and a core within the casing, the core having: a serpentine cooling passage; and at least one outlet passage fluidly connected with the serpentine cooling passage and the exhaust aperture, wherein the at least one outlet passage permits flow of a coolant from the serpentine cooling passage to the at least one exhaust aperture on the outer surface of the casing; and an airfoil connected with the base at a first end of the airfoil, the airfoil including: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side.