We present an investigation of the effect of ferromagnetic layer thickness on the exchange bias and coercivity enhancement in antiferromagnet/ferromagnet bilayers. At low temperatures both the exchange bias and coercivity closely follow an inverse thickness relationship, contrary to several recent theoretical predictions. Furthermore, the temperature dependence of the coercivity as a function of the ferromagnet thickness provides clear evidence for the existence of two distinct regimes. These regimes were probed with conventional magnetometry, anisotropic magnetoresistance, and polarized neutron reflectometry. At low thickness the coercivity exhibits a monotonic temperature dependence, whereas at higher thickness a broad maximum occurs in the vicinity of the Néel temperature. These regimes are delineated by a particular ratio of the ferromagnet to antiferromagnet thickness. We propose that the ratio of the anisotropy energies in the two layers determines whether the coercivity is dominated by the ferromagnetic layer itself or the interaction of the ferromagnetic layer with the antiferromagnet.