Combining Monte Carlo radiative transfer simulations and accurate 2D bulge/disc decompositions, we present a new study to investigate the effects of dust attenuation on the apparent structural properties of the disc and bulge of spiral galaxies. We find that dust affects the results from such decompositions in ways which cannot be identified when one studies dust effects on bulge and disc components separately. In particular, the effects of dust in galaxies hosting pseudo-bulges might be different from those in galaxies hosting classical bulges, even if their dust content is identical. Confirming previous results, we find that disc scale lengths are overestimated when dust effects are important. In addition, we also find that bulge effective radii and Sersic indices are underestimated. Furthermore, the apparent attenuation of the integrated disc light is underestimated, whereas the corresponding attenuation of bulge light is overestimated. Dust effects are more significant for the bulge parameters, and, combined, they lead to a strong underestimation of the bulge-to-disc ratio, which can reach a factor of two in the V band, even at relatively low galaxy inclinations and dust opacities. Nevertheless, it never reaches factors larger than about three, which corresponds to a factor of two in bulge-to-total ratio. Such effect can have an impact on studies of the black hole/bulge scaling relations. Comment: 11 pages, 5 figures (4 in color), 1 table; accepted for publication in MNRAS