Abstract We study the bi-drifting pulsar B1839-04, where the observed subpulse drift direction in the two leading pulse components is opposite from that in the two trailing components. Such diametrically opposed apparent motions challenge our understanding of an underlying structure. We find that for the geometry spanned by the observer and the pulsar magnetic and rotation axes, the observed bi-drifting in B1839-04 can be reproduced assuming a nondipolar configuration of the surface magnetic field. Acceptable solutions are found to either have relatively weak (∼1012 G) or strong (∼1014 G) surface magnetic fields. Our single-pulse modeling shows that a global electric potential variation at the polar cap that leads to a solid-body-like rotation of spark forming regions is favorable in reproducing the observed drift characteristics. This variation of the potential additionally ensures that the variability is identical in all pulse components resulting in the observed phase locking of subpulses. Thorough and more general studies of pulsar geometry show that a low ratio of impact factor to opening angle (β/ρ) increases the likelihood of bi-drifting to be observed. We thus conclude that bi-drifting is visible when our line of sight crosses close to the magnetic pole.