The driving and resistance torques of some rotating machinery for industrial applications are nonstationary and affect system dynamics. Under such operating conditions, coupling between torsional and lateral vibrations may become significant for drive lines supported by hydrodynamic bearings in particular design configurations. Indeed, the occurrence of fluid–structure interactions causes a reduction in the stability threshold of the journal bearings. A hypothesis based on Hopf bifurcation theory (HBT), which justifies how the coupling phenomenon develops, is validated by means of overall experimental observations and a suitable numerical model. When the pulsating driving torque induces significant angular speed oscillation, the rotor-bearing system lateral operating response becomes more complex, and bearing instability onset is detected. Such observation proves the influence of bearings in converting torsional oscillations to lateral vibrations. Particularly, during run-up and run-down tests, localized hysteresis is observed in trends of fundamental order contents. The numerical model of the hydrodynamic bearings solves the Reynolds equation in unsteady conditions to quantify the lateral vibrations amplitude in the presence of both angular speed oscillation and dynamic perturbation. The proposed approach proves the onset of torsional–lateral vibration coupling due to hydrodynamic bearings, to a certain extent. The detected hysteresis phenomena can also be explained by the onset of journal bearing instability.