The flow of segregated bidisperse assemblies of particles is of major importance for geophysical flows and bedload transport in particular. In the present paper, the mobility of strictly bidisperse segregated particle beds is studied with a coupled fluid discrete element method (DEM). Large particles are initially placed above small ones in a three-dimensional domain inclined at a slope of 10%. A gravity-driven water free surface flow induces a downslope shear-driven granular flow of the erodible bed. It is observed that, for the same water flow conditions, the bedload transport rate is higher in the bidisperse configuration than in the monodisperse one. Depending on the Shields number and on the depth of the interface between small and large particles, different transport phenomenologies are observed, ranging from no influence of the small particles to small particles reaching the bed surface due to diffusive remixing. In cases where the small particles hardly mix with the overlying large particles and for the range of studied size ratios (r < 4), it is shown that the increased mobility is not a bottom roughness effect, that would be due to the reduction of roughness of the underlying small particles, but a granular flow effect. This effect is analyzed within the framework of the mu(I) rheology, modeling the stress to strain rate relation for dense granular flows. It is demonstrated that the buried small particles are more mobile than larger particles and play the role of a "conveyor belt" for the large particles at the surface. Based on rheological arguments, a simple predictive model is proposed for the additional transport in the bidisperse case. It reproduces quantitatively the DEM results for a large range of Shields numbers and for size ratios smaller than 4. The results of the model are used to identify four different transport regimes of bidisperse mixtures, depending on the mechanism responsible for the mobility of the small particles. A phenomenological map is proposed for bidisperse bedload transport and, more generally, for any granular flow on an erodible bed.