Individual cells respond very differently to changes in environmental conditions. Stochasticity causes cells to respond at different times, magnitudes or both. Here we disentangle and quantify these two sources of heterogeneity. We track the adaptation dynamics of single Saccharomyces cerevisiae cells exposed to a nutrient shift from methionine to sulphate and back. Using single-molecule RNA fluorescence in situ hybridization, we count the number of transcripts of a methionine-biosynthesis enzyme in single cells during adaptation. The variation of response times between cells is small, yet we find a high transient variability in the messenger RNA copy numbers. Surprisingly, single cells display strongly delayed transcription induction, as we could induce transcription fourfold quicker by direct activation and bypassing the cellular control circuitry. Transcription repression occurs rapidly within several minutes. This study indicates that small variability in response timing combined with high, stochastic transcription activity can cause large cell-to-cell variability in dynamic adaptation responses.