Research on bedrock rivers primarily focused on bedrock incision and, to the best of our knowledge, morphodynamic models have not yet considered the variability of sediment grain size and the presence of small scale bedforms in low-slope (slope < 0.005) bedrock reaches. Further, very few models can quantify spatial and temporal changes in the fraction of channel bed covered with alluvium (alluvial cover) within these reaches. Here we present a novel formulation of alluvial morphodynamics of low-slope bedrock reaches transporting non-uniform bed material. The formulation is implemented in a one-dimensional model and validated against laboratory experiments on bedrock reaches downstream of stable alluvial-bedrock transitions, where the flow accelerates in space. The validated model is used to study the alluvial morphodynamics of bedrock reaches upstream of stable bedrock-alluvial transitions. Equilibrium results show that the interactions between flow, sediment transport and non-erodible bedrock surface result in a flow decelerating in the streamwise direction. The effects of this spatial flow deceleration are 1) a streamwise increase in alluvial cover, and 2) the formation of a pattern of downstream coarsening of bed surface sediment. We then investigated the effects of sea level rise/fall on the location of alluvial-bedrock and bedrock-alluvial transitions. In the case of sea level rise, alluvial-bedrock transitions migrate downstream and bedrock-alluvial transitions migrate upstream. Opposite migration directions are expected in the case of sea level fall.