For critical concrete infrastructure founded on bedrock, accurate characterization of high-frequency ground motions is essential. Predictions of hard rock site response based on empirical Ground-Motion Models (GMMs) for generic site conditions carry large uncertainties, as datasets used to develop GMMs often lack observations from hard-rock sites (Vs30 > 1500 m/s, time-averaged shear-wave velocity in the top 30 m). Current practice is to apply a Vs-kappa0 host-to-target correction, where Vs is the site shear-wave velocity profile and kappa0 is the near-surface high-frequency attenuation parameter. However, the reliability of these parameters for predicting appropriate site-response adjustment factors is poorly quantified and subject to large epistemic uncertainty. We apply an alternative framework to characterize hard-rock site response in Probabilistic Seismic Hazard Analysis (PSHA) using site-specific ground motion data. Our methodology relies on estimating the non-ergodic hard-rock site response at a given site using recorded ground motion data from dedicated seismic monitoring instrumentation. Using site-specific data allows us to remove the site-to-site variability component from PSHA and greatly reduce epistemic uncertainty in the hard-rock site response. We demonstrate the applicability of the proposed methodology for a critical facility in British Columbia, Canada. Comparison of the non-ergodic and Vs-kappa0-based hard-rock correction factors highlights the importance of compiling and using site-specific data in PSHA. For competent hard rock, we suggest that amplification at high frequencies is often controlled by factors other than impedance effects, such as topographic effects or near-surface high-frequency attenuation; these effects are not well captured by the traditional Vs-kappa0 approach.