It has been observed that the zonal drift velocity of equatorial plasma bubbles is generally eastward. However, it has not been well understood whether the zonal drift of plasma bubbles is the same as the ambient plasma drift and what process causes differences in the drift velocities of the ambient plasma and bubbles. In this study we analyze the ion drift velocities measured by the Defense Meteorological Satellites Program and ROCSAT-1 satellites and the electric fields measured by the Communications/Navigation Outage Forecasting System (C/NOFS) satellite in the presence of equatorial spread F. We find that the zonal drift velocity of the plasma particles inside plasma bubbles is significantly different from the ambient plasma drift. The relative zonal velocity of the ions inside the depletion region with respect to the ambient plasma is generally westward. In most cases it can be as high as several hundreds of meters per second. The plasma bubbles detected by the C/NOFS satellite in the midnight-dawn sector are still growing, and the polarization electric field inside the postmidnight bubbles is much stronger than the electric field in the ambient plasma. We suggest that the zonal drift velocity of the plasma particles inside the depletion region is driven by polarization electric field. When a plasma bubble is tilted, the E x B drift velocity caused by the polarization electric field has an upward component and a zonal component. Because of the zonal motion of the plasma particles inside the bubble, the eastward drift velocity of the bubble structure is faster than the ambient plasma drift for a west-tilted bubble and slower than the ambient plasma drift for an east-tilted bubble.