The flow in and around three-dimensional deformable bubbles subjected to a non-linear planar free shear layer was simulated using a finite difference/front tracking scheme with the full Navier-Stokes equations including surface tension. This allowed detailed resolution of the flow around and inside the bubble. The bubble size and response time is comparable to the thickness and timescale of the free shear layer and we have investigated increased deformation by systematically lowering surface tension. The interaction between the bubble wake and the shear layer led to complex three-dimensional flows past and within the bubble surface. The resulting hydrodynamic forces and trajectories of the fully resolved bubble simulation could be qualitatively compared with those expected from quasi-steady classical predictions. In general, the quasi-steady drag began to underpredict the actual drag as deformation increased and the quasi-steady lift predicted values of opposite sign to that of the actual lift for very high deformation.