  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 non-dipolar configuration
of the surface magnetic field. Acceptable solutions are found to either have
relatively weak $(\sim 10^{12} \,{\rm G})$ or strong $(\sim 10^{14} \,{\rm G})$
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 $(\beta /
\rho)$ 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.
