Genetically identical cells grown in the same culture display striking cell-to-cell heterogeneity in gene expression and other traits. A crucial challenge is to understand how much of this heterogeneity reflects the noise tolerance of a robust system and how much serves a biological function. In bacteria, stochastic gene expression results in cell-to-cell heterogeneity that might serve as a bet-hedging mechanism, allowing a few cells to survive through an antimicrobial treatment while others perish. Despite its clinical importance, the molecular mechanisms underlying bet hedging remain unclear. Here, we investigate the mechanisms of bet hedging in Saccharomyces cerevisiae using a new high-throughput microscopy assay that monitors variable protein expression, morphology, growth rate, and survival outcomes of tens of thousands of yeast microcolonies simultaneously. We find that clonal populations display broad distributions of growth rates and that slow growth predicts resistance to heat killing in a probabalistic manner. We identify several gene products that are likely to play a role in bet hedging and confirm that Tsl1, a trehalose-synthesis regulator, is an important component of this resistance. Tsl1 abundance correlates with growth rate and replicative age and predicts survival. Our results suggest that yeast bet hedging results from multiple epigenetic growth states determined by a combination of stochastic and deterministic factors.