Buoyancy driven turbulence due to heterogeneous bubble swarms are typically encountered in bubble columns operating in the dense heterogeneous regime. The integral scales of such turbulence are much larger than single bubble pseudo-turbulence. Accurate computational fluid dynamics predictions in this regime require correctly formulated anisotropic turbulence models with closures accounting for buoyancy driven turbulence effects. In the current study, a Reynolds-stress transport equation is formulated for bubbly flows from a hyperbolic two-fluid model by Reynolds averaging. The unclosed terms generated due to Reynolds averaging are quantified using high grid resolution, two-fluid simulations for bubbly flows in a periodic domain. The relative importance of the unclosed terms are discussed from a modeling stand point. The turbulence statistics, length and time scales, energy spectra, mean momentum budget and the Reynolds stress budget are analyzed for different bubble void fractions. The results show that the unclosed terms generated due to the averaging of Drag is significant in the liquid phase Reynolds Stress budget. Moreover, the unclosed terms generated due to the averaging of Drag, Virtual mass and Buoyancy are significant in the gas phase Reynolds Stress budget.