Bedload particles entrained by rivers tends to disperse as they move downstream. In this paper, we use the erosion-deposition model of Charru et al. (2004) to describe the velocity and the spreading of a plume of tracer particles. We restrict our analysis to steady-state transport above a flat bed of uniform sediment. The transport of tracer particles is then controlled by downstream advection and particle exchange with the immobile bed. After a transitional regime dominated by initial conditions, the evolution of a plume of markers tends asymptotically towards classical advection-diffusion: its average position grows linearly with time, whereas it spreads like the square root of time.