We report an extensive set of two-dimensional MHD simulations exploring the role and evolution of magnetic fields in the dynamics of supersonic plasma clumps. We examine the influence of both ambient field strength and orientation on the problem. Of those two characteristics, field orientation is far more important in the cases we have considered with β 0 = p g /p b ≥ 1. That is due to the geometry-sensitivity of field stretching/amplification from large-scale shearing motions around the bullet. When the ambient magnetic field is transverse to the bullet motion, even a very modest field, well below equipartition strength, can be amplified by field line stretching around the bullet within a couple of bullet crushing times so that Maxwell stresses become comparable to the ram pressure associated with the bullet motion. The possibility is discussed that those situations might lead to large, induced electric potentials capable of accelerating charged particles. When the ambient field is aligned to the bullet motion, on the other hand, reconnection-prone topologies develop that shorten the stretched field and release much of the excess energy it contains. In this geometry, the Maxwell stresses on the bullet never approach the ram pressure level. In both cases, however, the presence of a field with even moderate initial strength acts to help the flow realign itself around the bullet into a smoother, more laminar form. That reduces bullet fragmentation tendencies caused by destructive instabilities. Eddies seem less effective at field amplification than flows around the bullet, because fields within eddies tend to be expelled to the eddy perimeters. Similar effects cause the magnetic field within the bullet itself to be reduced below its initial value over time.For oblique fields, we expect that the transverse field cases modeled here are more generally relevant. What counts is whether field lines threading the face of the bullet are swept around it in a fashion that folds them (leading to reconnection) or