There is growing evidence showing that many critical biological processes are driven by biomolecule condensates through liquid-liquid phase separation (LLPS). Although the qualitative observation and description of LLPS have been well documented, quantitative simulations of the time-dependent progression of LLPS in live cells are generally lacking. In this work, we build a stochastic Monte Carlo model to simulate the dynamic LLPS process during the formation of bacterial aggresomes. We demonstrate that the size distribution of the protein condensates evolves from an exponential-like to a bimodal-like pattern, and the number of condensates increases at the beginning and then decreases after reaching a maximum. Incorporating diffusion and collision, our simplified model recapitulates the two-step LLPS process in which many smaller condensates are formed in the first step and then merged into a few larger ones. We further reveal that the condensation speed, which can be defined by the condensates formed in unit time during the first step, is mainly determined by both the collision energy barrier and the initial protein density, while the number of condensates at the equilibrium is mainly associated with the dissociation energy barrier. Moreover, the LLPS process is not sensitive to temperature changes ranging around physiological conditions. Additionally, we consider the effect of the nucleation energy barrier on LLPS. We find that a higher nucleation energy barrier brings a slower condensation speed. Overall, we simulate the spatiotemporal dynamics of the LLPS process and provide qualitative guidance for understanding the dynamics of LLPS in bacterial cells, which can faithfully recapitulate experimental observations and facilitate the design of future experimental tests.