We report on the stabilization of ferromagnetic skyrmions in zero external magnetic fields, in exchange-biased systems composed of ferromagnetic-antiferromagnetic (FM-AFM) bilayers. By performing atomistic spin dynamics simulations, we study cases of compensated, uncompensated, and partly uncompensated FM-AFM interfaces, and investigate the impact of important parameters such as temperature, inter-plane exchange interaction, Dzyaloshinskii-Moriya interaction, and magnetic anisotropy on the skyrmions appearance and stability. The model with an uncompensated FM-AFM interface leads to the stabilization of individual skyrmions and skyrmion lattices in the FM layer, caused by the effective field from the AFM instead of an external magnetic field. Similarly, in the case of a fully compensated FM-AFM interface, we show that FM skyrmions can be stabilized. We also demonstrate that accounting for interface roughness leads to stabilization of skyrmions both in compensated and uncompensated interface. Moreover, in bilayers with a rough interface, skyrmions in the FM layer are observed for a wide range of exchange interaction values through the FM-AFM interface, and the chirality of the skyrmions depends critically on the exchange interaction.