The strength, or stiffness Kud, of the magnetic unidirectional anisotropy in Co (90-300 Å)/CoO bilayers has been studied with ac susceptometry. We develop a model to describe the ac susceptibility which indicates that the stiffness Kud decreases linearly with temperature as (1 - T/Tcrit). As the temperature increases and Kud decreases, a rotation of the magnetization to a uniaxial easy direction is observed. The values of Kud determined by this small amplitude field oscillation technique are found to be larger than the values obtained when evaluated by the usual hysteresis loop technique. We observe that the exchange field, Hex, could be greatly enhanced and its deterioration after repeated magnetization reversals significantly reduced by partially capping the Co surface prior to oxygen exposure.