MOTIVATION: Gene expression is characterised by stochastic bursts of transcription that occur at brief and random periods of promoter activity. The kinetics of gene expression burstiness differs across the genome and is dependent on the promoter sequence, among other factors. Single-cell RNA sequencing (scRNA-seq) has made it possible to quantify the cell-to-cell variability in transcription at a global genome-wide level. However, scRNA-seq data is prone to technical variability, including low and variable capture efficiency of transcripts from individual cells. RESULTS: Here, we propose a novel mathematical theory for the observed variability in scRNA-seq data. Our method captures burst kinetics and variability in both the cell size and capture efficiency, which allows us to propose several likelihood-based and simulation-based methods for the inference of burst kinetics from scRNA-seq data. Using both synthetic and real data, we show that the simulation-based methods provide an accurate, robust and flexible tool for inferring burst kinetics from scRNA-seq data. In particular, in a supervised manner, a simulation-based inference method based on neural networks proves to be accurate and useful when applied to both allele and non-allele-specific scRNA-seq data. AVAILABILITY: The code for Neural Network and Approximate Bayesian Computation inference is available at https://github.com/WT215/nnRNA and https://github.com/WT215/Julia_ABC respectively. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.