Climate change is drastically changing the timing of biological events across the globe. Changes in the phenology of seasonal migrations between the breeding and wintering grounds have been observed across biological taxa, including birds, mammals, and insects. For birds, strong links have been shown between changes in migration phenology and changes in weather conditions at the wintering, stopover, and breeding areas. For other animal taxa, the current understanding of, and evidence for, climate (change) influences on migration still remains rather limited, mainly due to the lack of long‐term phenology datasets. Bracken Cave in Texas (USA) holds one of the largest bat colonies of the world. Using weather radar data, a unique 23‐year (1995–2017) long time series was recently produced of the spring and autumn migration phenology of Brazilian free‐tailed bats (Tadarida brasiliensis) at Bracken Cave. Here, we analyse these migration phenology time series in combination with gridded temperature, precipitation, and wind data across Mexico and southern USA, to identify the climatic drivers of (changes in) bat migration phenology. Perhaps surprisingly, our extensive spatiotemporal search did not find temperature to influence either spring or autumn migration. Instead, spring migration phenology seems to be predominantly driven by wind conditions at likely wintering or spring stopover areas during the migration period. Autumn migration phenology, on the other hand, seems to be dominated by precipitation to the east and north‐east of Bracken Cave. Long‐term changes towards more frequent migration and favourable wind conditions have, furthermore, allowed spring migration to occur 16 days earlier. Our results illustrate how some of the remaining knowledge gaps on the influence of climate (change) on bat migration and abundance can be addressed using weather radar analyses.