Halide double perovskites have gained significant attention, owing to their composition of low-toxicity elements, stability in air, and recent demonstrations of long charge-carrier lifetimes that can exceed 1 s. In particular, Cs2AgBiBr6 has been the subject of many investigations in photovoltaic devices. However, the efficiencies of solar cells based on this double perovskite are still far from the theoretical efficiency limit of the material. Here, we investigate the role of grain size on the optoelectronic properties of Cs2AgBiBr6 thin films. We show through cathodoluminescence measurements that grain boundaries are the dominant non-radiative recombination sites. We also demonstrate through field-effect transistor and temperature-dependent transient current measurements that grain boundaries act as the main channels for ion transport. Interestingly, we find a positive correlation between carrier mobility and temperature, which resembles the hopping mechanism often seen in organic semiconductors. These findings explain the discrepancy between the long diffusion lengths >1 m found in Cs2AgBiBr6 single crystals versus the limited performance achieved in their thin film counterparts. Our work shows that mitigating the impact of grain boundaries will be critical for these double perovskite thin films to reach the performance achievable based on their intrinsic single-crystal properties.