The exchange bias of epitaxially grown CoO/Fe/Ag(001) was investigated using x-ray magnetic circular dichroism and x-ray magnetic linear dichroism (XMLD) techniques. A direct XMLD measurement on the CoO layer during the Fe magnetization reversal shows that the CoO compensated spins are rotatable at thinner thickness and frozen at larger thickness. By a quantitative determination of the rotatable and frozen CoO spins as a function of the CoO film thickness, we find the remarkable result that the exchange bias is well established before frozen spins are detectable in the CoO film. We further show that the rotatable and frozen CoO spins are uniformly distributed in the CoO film.