A discrete vortex model is used to approximate adequately large eddy features in turbulent free shear flows and the effects of two-way mass and momentum coupling on Lagrangian bubble trajectories and dispersion in such eddy structures are investigated. The number of bubbles introduced into the flow is sufficiently large enough for cumulative effects of bubbles to influence the flow but is still small enough so that bubble-bubble interactions can be neglected. It is demonstrated that for two-way coupling case, a reduction in the magnitude of the vorticity and pressure gradients around the large-scale vortex centre is observed. In addition to modification of the vortex structures, it is found that the tendency of the accumulation of bubbles becomes weaker in comparison to the one-way coupling case. In seeking quantification of the bubble dispersion, the Eulerian approach based on the bubble number fluxes at different downstream cross-sections of the mixing layer in terms of ensemble trajectory statistics and Lagrangian approach based on the bubble mean square displacement are adopted. It is observed that the ensemble average flux profiles of bubbles for two-way coupling case are farther skewed towards the high-speed stream of the shear layer in contrast to its one-way coupling case.