The cooling field dependence of the exchange bias field in ferromagnet/antiferromagnet (FM/AF) multilayers demonstrates that the bulk AF spin structure plays a crucial role on the origin of exchange bias. FM/AF/FM trilayers were designed to eliminate any interlayer exchange coupling between the FM slabs. By choosing the magnetic cooling field, the AF is ordered below its Néel temperature with the FM layers fully saturated either parallel or antiparallel to each other. The significant difference in the exchange bias field between these two cooling configurations confirms that exchange bias cannot be a purely interfacial effect and that the bulk AF moments play a significant role in pinning the uncompensated spins at the AF/FM interface. This experiment also demonstrates that the mechanism responsible for coercivity enhancement has a different origin and is independent of the process that gives rise to exchange bias.