Meteorological drought serves as a precursor to hydrological drought, and understanding the dynamic propagation process from meteorological to hydrological drought is crucial for developing hydrological drought forecasting. Due to the complexity of physical processes involved in drought propagation, the spatiotemporal aspects of this phenomenon are not fully understood. In this study, weekly-scale SPI, SPEI, and SSI indices are employed, along with run theory and Bayesian network analysis, to explore the characteristics and temporal variations of different drought events. The aim is to unveil the temporal patterns of meteorological drought transitioning into hydrological drought. The results reveal the following: (1) The response of hydrological drought to meteorological drought in the Poyang Lake Basin typically occurs within 11 to 15 weeks, with higher correlations between meteorological and hydrological droughts during summer and autumn than in spring and winter. (2) After a meteorological drought event, hydrological drought occurs in over 80% of cases. Under certain levels of meteorological drought, the most probable event is a hydrological drought of the same level, followed by a hydrological drought one level lower than the meteorological drought. (3) The higher the level of meteorological drought that evolves into hydrological drought, the longer the time interval. Mild meteorological droughts are challenging to evolve into severe hydrological droughts. The time interval for drought propagation is longer in spring and winter compared to summer and autumn.