Recent investigations of magnetic vortices in ferromagnetic (FM)∕antiferromagnetic bilayer circular dots show that a magnetic vortex pattern can be imprinted in the antiferromagnet when the bilayers are cooled through the blocking temperature of the system after setting the magnetic state in the FM. Here we investigate the effects of the patterned pinning profile on the magnetization dynamics of these exchange-biased magnetic vortices. A magnetic vortex in a micron-sized magnetically soft element exhibits a low-frequency translational dynamic mode and, since the frequency of this mode is defined by the shape of the energy profile of a displaced vortex, the addition of a vortex-shaped pinning-field profile should influence its motion. Micromagnetic simulations show that the frequency scales linearly with the magnitude of the local pinning field. In a 500 nm permalloy dot, 15 nm thick, a more than twofold increase in the frequency is expected for experimentally realizable exchange-bias fields.