This Letter reports on the exchange coupling between nanometric Co clusters and disordered MnPt thin films. It is found that, under field-cooling, the MnPt develops a bulk magnetization M_{AF}. The correlation between M_{AF} and the exchange bias H_{b} is studied using a different field-cooling procedure. From this, using a mean-field approach, it is shown that the effective field acting on the interface magnetization responsible for H_{b} is proportional to M_{AF}. This results is strong evidence in favor of the domain state model for exchange bias, in which H_{b} is correlated with the bulk magnetic state of the antiferromagnet, and not only restricted to its interface configuration.