The full Navier-Stokes equations were employed with a single-fluid model and a front tracking scheme to study a large cylindrical bubble in a free shear layer. A general formulation based on work by Auton et al. of the hydrodynamic forces on a finite Reynolds number large bubble in an unsteady, nonuniform and rotational flow was then used to investigate the effects of nonlinear spatial and temporal gradients on dispersion. The resulting bubble dispersion in the full Navier-Stokes solution significantly differ from that by a conventional bubble dynamic equation based on linear spatial gradients and quasi-steady flow. This was due to the adjunct forces not accounted for by such a formulation, which are related to regions of high nonuniformity and unsteadiness. These adjunct forces in the drag/lift direction were correlated with rapid variations of relative bubble velocity and high gradients of the liquid velocity.