This study examines the propagation from meteorological to hydrological drought across representative river basins in Bulgaria, focusing on temporal and spatial characteristics of the process. Monthly precipitation and streamflow data for 1964–2023 were used to calculate the Standardized Precipitation Index (SPI-1 to SPI-12) and the Streamflow Drought Index (SDI-1). The results indicate an increase in drought frequency and severity during 1994–2023 compared to 1964–1993, particularly at longer accumulation scales (SPI-6 to SPI-12). The strongest relationships between meteorological and hydrological drought are observed at multi-seasonal scales (SPI-3 to SPI-6), while clear seasonal differences are identified between the cold (November–April) and warm (May–October) half-years. Conditional probability analysis shows a common propagation lag of 7–9 months across the studied basins. At the same time, once critical precipitation deficits are reached, hydrological drought may develop at short lags of 0–1 month, indicating a rapid system response under severe conditions. Marked regional differences are observed. The middle and lower Struma basin shows the highest drought-transition probabilities (>50%), whereas the Tundzha basin appears more buffered due to reservoir regulation and hydrogeological conditions. The results highlight that drought propagation depends on accumulation time, seasonal regime, and basin characteristics, and they support the need for basin-specific and proactive water management under changing climate conditions.