In Co/CoO bilayers separation of the unidirectional anisotropy energy from crystalline anisotropy is accomplished with the temperature variation of the ac susceptibility from room temperature to 4.2 K. Measurements above the blocking temperature of the CoO layer give a clear measure of crystalline anisotropy in the Co. At 4.2 K 85% of the total anisotropy is from K-ud while the anisotropy of the Co layer only contributes about 15%. The small crystalline anisotropy energy does not account for the large difference between the exchange anisotropy determined by ac susceptibility and hysteresis loops.