Hydrodynamic bearings are widely used across a broad range of machinery due to their versatility and efficiency. Despite their numerous advantages, rotors supported by fluid-film bearings are prone to unique dynamic phenomena arising from the interaction between the rotating fluid and the shaft. These phenomena are categorized into two distinct types: oil-whirl and oil-whip. The phenomenon of fluid-induced instability can be analyzed through the framework of bifurcation theory, specifically as a Hopf bifurcation, which may be either supercritical or subcritical. In the case of a supercritical Hopf bifurcation, the system exhibits oil-whirl, characterized by the emergence of stable limit cycles beyond the instability onset speed. Conversely, a subcritical Hopf bifurcation corresponds to oil-whip, where unstable limit cycles are created. Therefore, identifying the type of Hopf bifurcation provides insight into whether the system will experience oil-whirl or oil-whip. This work introduces an approach for predicting Hopf bifurcations in rotor systems using the Center Manifold Reduction (CMR) method. The approach involves deriving the center manifold of the bifurcating system and analyzing it to determine whether the system will exhibit oil-whirl or oil-whip behavior. The primary contribution of this work is the application of the parameterization method for invariant manifolds to derive the center manifold of the system. The results consist of a comparison between the predicted bifurcations and the responses measured in the experimental setup, demonstrating that CMR can be reliably used to predict whether the system exhibits oil-whirl or oil-whip.