Air foil bearings (AFBs) have found many successful applications in small high-speed oil-free turbomachinery over the past decades. AFBs are made of a thin top foil serving as the bearing surface, and an underlying mechanical structure that provides structural support and damping. AFBs offer better rotor stability than the rigid-walled gas bearings because of the damping. However, improvements in the damping and the rotordynamic stability are still active areas of research in the AFBs. Researchers have suggested different solutions for improving the stability such as hydrodynamic preload, pressurized air injection, forced axial flow, different material structures, etc. This study investigates the effect of the added bump foil damper around the bearing sleeve on the rotordynamic performance of a rigid rotor (3.91 kg) supported by AFBs (49mm in diameter and 37.5mm in length). Simulation studies involve transient time-domain simulation of the rotor's vibrational motion under the imbalance excitation with different sleeve masses and different stiffness of the bump foil damper. From the simulation results, the beneficial effect of the added bump foil damper on the rotordynamic performance of the rotor was observed. By reducing the stiffness of the damper, the stability increases and the onset speed of the subsynchronous vibration pushes to the higher speeds. Also, a heavier bearing sleeve reduces the magnitude of the vibration at the critical speed. Two radial AFBs with the damper around the bearing sleeve support the rotor. Two different bump foil dampers were manufactured using different material thicknesses, and two sets of bearing sleeves were made from different materials with identical geometries to investigate the effect of the bearing sleeve mass on the rotordynamic performance.