During high-speed operations, severe structural vibration due to rotor flexibility becomes one of key issues that can limit the performance and duty cycle of a rotating machinery, so an effective vibration suppression method needs to be developed for such a rotating system. In addition, the gyroscopic effect associated with uncertainties in disc offset of a rotor system can lead to an increase of the rotor whirl frequency and a variation in rotor dynamic characteristics. The present study thus focuses on developing an active control method using active lateral bearings that can regulate bearing forces via active modification of bearing lateral displacements so an effective actuation mechanism for a rotating rotor can be achieved. The gyroscopic effect on the rotor vibration is considered in the active control development by considering it as an internal disturbance affecting the internal dynamics of the rotor system. An Extended State Observer (ESO) is developed for estimating the system's states and generalized disturbance that consists of uncertainties associated with internal dynamics and external forces affecting the rotor vibration. Active Disturbance Rejection Control (ADRC) method with the developed ESO is implemented using active bearings to suppress rotor vibration to achieve satisfactory control robustness against the internal and external uncertainties, particularly the uncertainties associated with the gyroscopic effect. The control robustness with respect to uncertainties in the disc eccentricity and offset, which can lead to a variation of the gyroscopic effect, is investigated, demonstrating the effectiveness of the developed active control method for suppressing rotor vibration.