Current riverine plastic monitoring best practices mainly consider surface observations, thus neglecting the underlying distribution of plastics in the water column. Bias on plastic budgets estimations hinders advances on modelling and prediction of plastics fate. Here, we experimentally disclose the structure of plastics transport in surface water flows by investigating how thousands of samples of plastics commonly found in fluvial environments travel in turbulent river flows. We show for the first time that surface tension plays a key role in the transport of plastics since its effects can be of the same magnitude as buoyancy and turbulence, therefore holding a part of the dispersed buoyant plastics captive by the water surface. We investigate two types of transport; surfaced plastics (surface tension-turbulence-buoyancy dominated), in contact with the free surface, and suspended plastics (turbulence-buoyancy dominated). We prove that this duality in transport modes is a major source of error in the estimation of plastic budgets, which can be underestimated by 90 % following current, well-established monitoring protocols if sampling is conducted solely in the water surface. Based on our empirical findings, we optimize physics-driven monitoring strategies for plastic fluxes in rivers, thereby achieving over a ten-fold reduction of the bias and uncertainty of riverine plastic pollution estimates.