The non-resonant (Bell) streaming instability driven by energetic particles is crucial for producing amplified magnetic fields that are key to the acceleration of cosmic rays (CRs) in supernova remnants, around Galactic and extra-galactic CR sources, and for the CR transport. We present a covariant theory for the saturation of the Bell instability, substantiated by self-consistent kinetic simulations, that can be applied to arbitrary CR distributions and discuss its implications in several heliospheric and astrophysical contexts.