We report a stable and efficient complex Langevin sampling scheme for performing approximation-free numerical simulations directly on the path-integral coherent-states field theory for an assembly of interacting bosons. We apply the method to generate the λ line of critical phase transitions associated with Bose-Einstein condensation in a model ϕ^{4} scalar field theory. The new approach enjoys near-linear scaling in the resolved (d+1) spatial and imaginary-time dimensions and should be particularly efficient for the study of dense systems at low temperature.