Graphene films with high content of bilayer graphene are obtained by chemical vapor deposition technique on copper (Cu) foil by means of suitably designing the flux geometries of the reactant gases. First single-layer graphene growth is optimized using a preliminary oxygen passivation of the Cu substrate which facilitates the formation of larger graphene grains with low defect density. Then, in order to enhance the transport of reactant species to the catalyst substrate, the gas flux geometry is modified in two ways: (i) fixing a graphite holder next to the Cu substrate perpendicular to the stream of the flux gases or (ii) positioning the Cu foil into a graphite shelter. It is found that both modifications facilitate the growth of a second graphene layer leading to increased formation of bilayer graphene. The obtained graphene layers are characterized by Raman spectroscopy (with special focus on the overtone (2D) of the disorder-induced band), scanning electron microscopy, transmission electron microscopy, atomic force microscope analysis and optical transmission measurements. Narrow symmetric 2D Raman peaks with linewidths ranging down to 22 cm−1 but blue-shifted with respect to that of single-layer graphene are obtained from graphite holder- and shelter-grown samples indicating high-quality bilayer graphene.