We numerically investigated the transport of a passive colloidal particle in a one-dimensional periodic array of planar counter-rotating convection rolls at high Péclet numbers. We show that advection-enhanced diffusion is drastically suppressed by an external transverse bias but strongly reinforced by a longitudinal drive of appropriate intensity. Both effects are magnified by imposing free-slip flows at the array's edges. The dependence of the diffusion constant on an external forcing is interpreted as a measure of the fluid-mechanical robustness of the flow boundary layer mechanism governing diffusion in convection rolls.