Mitogen-activated protein kinase (MAPK) cascades are conserved signalling modules that control many cellular processes by integrating intra- and extracellular cues. The p38/Hog1 MAPK is transiently activated in response to osmotic stress, leading to rapid translocation into the nucleus and induction of a specific transcriptional program. When investigating the dynamic interplay between Hog1 activation and Hog1-driven gene expression, we found that Hog1 activation increases linearly with stimulus, whereas the transcriptional output is bimodal. Modelling predictions, corroborated by single cell experiments, established that a slow stochastic transition from a repressed to an activated transcriptional state in conjunction with transient Hog1 activation generates this behaviour. Together, these findings provide a molecular mechanism by which a cell can impose a transcriptional threshold in response to a linear signalling behaviour.