Hydrogen permeation into mirrors used in extreme ultraviolet lithography results in the formation of blisters, which are detrimental to reflectivity. An understanding of the mechanism via which hydrogen ends up at the interface between the top ruthenium layer and the underlying bilayers is necessary to mitigate the blistering damage. In this study, we use density functional theory to examine the ways in which hydrogen, having entered the near-surface interstitial voids, can migrate further into the metal or to its surface. We show that with hydrogen and tin adsorbed on the ruthenium surface, diffusion to the surface is blocked for interstitial hydrogen in the metal, making diffusion further into the metal more likely than out-diffusion. The dependence on surface conditions matches and confirms similar findings on hydrogen permeation into metals. This suggests control and modification of surface conditions as a way to influence hydrogen retention and blistering.