Understanding the long-term variability of reference evapotranspiration (ETo) is crucial for effectively managing water use and implementing coherent regulations for agricultural cropping systems. However, in the context of climate change, there has been a lack of study on the factors that influence ETo in a sub-tropical country like Bangladesh. To fill this gap, the present study investigates the long-term variability of ETo in Bangladesh using the FAO56 Penman–Monteith model. Analyzing data from 18 weather sites (1980–2017), we found a significant decline in ETo with an average decline of 0.1089 mm per decade, primarily influenced by temperature (T) and sunshine duration (SSD). The Marlet wavelet analysis showed that ETo experienced 3–7 significant oscillation cycles with frequency bands of 1–3 years from 1988 to 1994, which played a crucial role in determining the features of ETo evolution. The annual mean ETo showed a substantial positive correlation with T and SSD (p < 0.05) and a significant negative correlation with relative humidity. Regional variations in sensitivity coefficients indicate complicated spatial changes in ETo dynamics. The analysis of contribution rates reveals that SSD significantly impacts the changes in ETo trends over all seasons, except for the post-monsoon period when T emerges as the primary driver. This quantitative analysis of periodic oscillations and factors influencing ETo at a spatiotemporal scale was a scientific foundation for making informed decisions about regulating agricultural production, climate change adaptation, and sustainable water resource management. These findings provide critical insights for sustainable water resource management in agriculture under changing climate conditions.