The random utility model is the standard empirical framework for modelling stochastic choice behaviour in applied settings. In this framework, the distribution of random utility has important implications both for testing behavioural theories and predicting behaviour, however the theoretical and empirical foundations of this distribution are not well understood. Moreover, the random utility framework has so far been agnostic about the dynamics of the decision process that are of considerable interest in psychology and neuroscience, captured by a class of bounded accumulation models which relate decision times to stochastic behaviour. We demonstrate that the random utility model can be derived from a bounded accumulation model, of which the classic drift diffusion model is a special case. The features of this dynamic process impact the distributional structure of random utility and potentially bias estimates of structural choice parameters. Finally, the article demonstrates how particular features of the bounded accumulation frameworks can constrain the distribution of random utility, offering advances in modelling choice behaviour.