<p>Einstein’s stochastic bedload transport framework often underperforms near incipient motion because of simplified representations of particle step length and sediment pick-up probability. To address this issue, a two-stage single-particle model is developed in which bedload motion is represented by a contact phase (rolling) followed by a detachment phase (saltation), while grain protrusion is incorporated through bed-surface protrusion statistics. The model clarifies how protrusion, sediment specific gravity, and near-bed velocity fluctuations influence the step length to particle size ratio. The predicted mean step length, together with a near-threshold closure for pick-up probability, is then embedded into Einstein’s stochastic framework to derive a corrected bedload transport function. The resulting formulation improves predictions for uniform sediments near incipient motion and remains applicable to fully rough flows without the need for additional fitting parameters. This framework is most relevant to gravel-bed rivers and mountain streams where near-threshold transport influences bed stability and sediment budgets.</p>