Mechanisms that control cell-to-cell variation in gene expression ('phenotypic variation') can determine a population's growth rate, robustness, adaptability and capacity for complex behaviours. Here we describe a general strategy (termed FABMOS) for tuning the phenotypic variation and mean expression of cell populations by modulating the frequency and bias of stochastic transitions between 'OFF' and 'ON' expression states of a genetic switch. We validated the strategy experimentally using a synthetic fim switch in Escherichia coli. Modulating the frequency of switching can generate a bimodal (low frequency) or a unimodal (high frequency) population distribution with the same mean expression. Modulating the bias as well as the frequency of switching can generate a spectrum of bimodal and unimodal distributions with the same mean expression. This remarkable control over phenotypic variation, which cannot be easily achieved with standard gene regulatory mechanisms, has many potential applications for synthetic biology, engineered microbial ecosystems and experimental evolution.