Shear flows in turbulent fluids have been known to act as transport barriers for some time. An example of a shear flow generating mechanism is the E×B shear in plasma, which has a substantial impact on the dynamics of magnetic confinement fusion devices. The influence of this may be seen in the scrape-off layer (SOL) where blobs or filaments may be sheared and velocity impacted, and in the edge and core of the plasma, where the formation of transport barriers and suppression of turbulence is strongly associated with such shearing effects. A dynamical picture of transport through these effects has been elusive, and so we consider the application of an ’observational’ random walk to such transport. The ’observational’ random walk is modification of the random walk approach, introducing an intrinsic time separating observations, which reproduces the basic results of previous random walk models given a Gaussian jump function. Using a test case of synthetic turbulence, we demonstrate that the jump function can be inferred from the statistics of passive particles propagated by E × B drift on a synthetic turbulence field, and that the transport equation found from the jump function matches the expected diffusive transport very well. We then consider passive particles on simulations of the classic and modified Hasagawa-Wakatani equations for a variety of adiabaticity values, and find normal transport in the near-hydrodynamic limit. When zonal flows appear, we find jump functions with non-Gaussian features, which result in transport equations with fractional differential terms in addition to, or in place of, diffusion terms. We surmise that the non-local fractional terms are related to the zonal flows acting as transport barriers.