Transcription of almost all mammalian genes occurs in stochastic bursts, however the fundamental control mechanisms that allow appropriate single-cell responses remain unresolved. Here we utilise single cell genomics data and stochastic models of transcription to perform global analysis of the toll-like receptor (TLR)-induced gene expression variability. Based on analysis of more than 2000 TLR-response genes across multiple experimental conditions we demonstrate that the single-cell, gene-by-gene expression variability can be empirically described by a linear function of the population mean. We show that response heterogeneity of individual genes can be characterised by the slope of the mean-variance line, which captures how cells respond to stimulus and provides insight into evolutionary differences between species. We further demonstrate that linear relationships theoretically determine the underlying transcriptional bursting kinetics, revealing different regulatory modes of TLR response heterogeneity. Stochastic modelling of temporal scRNA-seq count distributions demonstrates that increased response variability is associated with larger and more frequent transcriptional bursts, which emerge via increased complexity of transcriptional regulatory networks between genes and different species. Overall, we provide a methodology relying on inference of empirical mean-variance relationships from single cell data and new insights into control of innate immune response variability.