We present a mechanism for the recently discovered magnetoresistance in disordered pi-conjugated materials, based on hopping of polarons and bipolaron formation, in the presence of the random hyperfine fields of the hydrogen nuclei and an external magnetic field. Within a simple model we describe the magnetic field dependence of the bipolaron density. Monte Carlo simulations including on-site and longer-range Coulomb repulsion show how this leads to positive and negative magnetoresistance. Depending on the branching ratio between bipolaron formation or dissociation and hopping rates, two different line shapes in excellent agreement with experiment are obtained.