Optically Stimulated Luminescence (OSL) dating has enormous potential for interpreting fluvial sediments, because the mineral grains used for OSL dating are abundant in fluvial deposits. However, the limited light exposure of mineral grains during fluvial transport and deposition often leads to scatter and inaccuracy in OSL dating results. Here we present a statistical protocol which aims to overcome these difficulties. Rather than estimating a single burial age for a sample, we present ages as likelihood functions created by bootstrap re-sampling of the equivalent-dose data. The bootstrap likelihoods incorporate uncertainty from age-model parameters and plausible variation in the input data. This approach has the considerable advantage that it permits Bayesian methods to be used to interpret sequences containing multiple samples, including partially bleached OSL data. We apply the statistical protocol to both single-grain and small-aliquot OSL data from samples of recent fluvial sediment. The combination of bootstrap likelihoods and Bayesian processing may greatly improve OSL chronologies for fluvial sediment, and allow OSL ages from partially bleached samples to be combined with other age information.