We present results of MD simulations of low energy He ion bombardment of low density fuzz in bcc elements. He ions can penetrate several micrometers into sparse fuzz, which allows for a sufficient He flux through it to grow the fuzz further. He kinetic energy falls off exponentially with penetration depth. A BCA code was used to carry out the same ion bombardment on the same fuzz structures as in MD simulations, but with simpler, 10 million times faster calculations. Despite the poor theoretical basis of the BCA at low ion energies, and the use of somewhat different potentials in MD and BCA calculations, the ion penetration depths predicted by BCA are only ∼12% less than those predicted by MD. The MD-BCA differences are highly systematic and trends in the results of the two methods are very similar. We have carried out more than 200 BCA calculation runs of ion bombardment of fuzz, in which parameters in the ion bombardment process were varied. For most parameters, the results show that the ion bombardment process is quite generic. The ion species (He or H), ion mass, fuzz element (W, Ta, Mo, Fe) and fuzz element lattice parameter turned out to have a modest influence on ion penetration depths at most. An off-normal angle of incidence strongly reduces the ion penetration depth. Increasing the ion energy increases the ion penetration, but the rate by which ion energy drops off at high ion energies follows the same exponential pattern as at lower energies.