We propose a new bubble dynamics model to study the evolution of a suspension of bubbles over a wide range of vesicularity, and that accounts for hydrodynamical interactions between bubbles while they grow, deform under shear flow conditions, and exchange mass by diffusion coarsening. The model is based on a lattice Boltzmann method for free surface flows. As such, it assumes an infinite viscosity contrast between the exsolved volatiles and the melt. Our model allows for coalescence when two bubbles approach each other because of growth or deformation. The parameter (disjoining pressure) that controls the coalescence efficiency, i.e., drainage time for the fluid film between the bubbles, can be set arbitrarily in our calculations. We calibrated this parameter by matching the measured time for the drainage of the melt film across a range of Bond numbers (ratio of buoyancy to surface tension stresses) with laboratory experiments of a bubble rising to a free surface. The model is then used successfully to model Ostwald ripening and bubble deformation under simple shear flow conditions. The results we obtain for the deformation of a single bubble are in excellent agreement with previous experimental and theoretical studies. For a suspension, we observe that the collective effect of bubbles is different depending on the relative magnitude of viscous and interfacial stresses (capillary number). At low capillary number, we find that bubbles deform more readily in a suspension than for the case of a single bubble, whereas the opposite is observed at high capillary number.