Plasma bubbles in the ionosphere have a significant effect on radio wave communication and navigation. Under the worst condition, it will fail to function the systems relying on the ionosphere. On the other hand, the physical mechanisms of evolution and diurnal variations of the plasma bubbles in the ionosphere are still unclear. Therefore, it is still worthy to simulate the plasma bubbles in the ionosphere for radio wave propagation and science. In this study, the equatorial plasma bubbles induced by one- and two- dimensional disturbance in the ionosphere are simulated, where traveling ionospheric disturbance (TID) is used to produce the two-dimensional disturbance in the ionosphere. The dispersion relationship of gravity wave is used to represent the corresponding wavelength of TID in this study. More importantly, we investigate the effect of recombination rate on the development of plasma bubbles by numerical simulation. The simulation results show that the recombination rate of the plasma in the ionosphere has a significant effect on the development of plasma bubbles. The greater the recombination rate, the more time it takes to produce the plasma bubbles. For one-dimensional disturbance in the ionosphere, there is no significant effect in the structure of plasma bubbles for the recombination rate of the plasma. However, the recombination rate plays a significant effect on the structure of plasma bubbles induced by TID. When the recombination rate is less in numerical simulation, the complex structure including bifurcation, plume-like structures, and pinching of plasma bubbles can occur in the development of bubbles. In contrast, the structure of plasma bubbles is simpler when the recombination rate is greater in simulation. As a result, the recombination rate of the plasma is a significant factor for simulating the plasma bubbles in the ionosphere. The greater recombination rate can result in the slowing down of equatorial plasma bubbles and the simplifying the structure of the bubbles as well. In addition, it is found that not all of plasma bubbles at the bottom of the ionosphere can grow to the top of the ionosphere when many bubbles occur on the bottom side. The direction of the polarization electric field near the bubbles can be changed in the non-linear development of the bubbles. Therefore, only the bubbles where the polarization electric field is always eastward can develop to the topside.