We present the results of two-component (disc+bar) and three-component (disc+bar+bulge) multiwavelength 2D photometric decompositions of barred galaxies in five SDSS bands (ugriz). This sample of ∼3,500 nearby (z < 0.06) galaxies with strong bars selected from the Galaxy Zoo citizen science project is the largest sample of barred galaxies to be studied using photometric decompositions which include a bar component. With detailed structural analysis we obtain physical quantities such as the bar- and bulge-to-total luminosity ratios, effective radii, Sérsic indices and colours of the individual components. We observe a clear difference in the colours of the components, the discs being bluer than the bars and bulges. An overwhelming fraction of bulge components have Sérsic indices consistent with being pseudobulges. By comparing the barred galaxies with a mass-matched and volume-limited sample of unbarred galaxies, we examine the connection between the presence of a large-scale galactic bar and the properties of discs and bulges. We find that the discs of unbarred galaxies are significantly bluer compared to the discs of barred galaxies, while there is no significant difference in the colours of the bulges. We find possible evidence of secular evolution via bars that leads to the build-up of pseudobulges and to the quenching of star formation in the discs. We identify a subsample of unbarred galaxies with an inner lens/oval and find that their properties are similar to barred galaxies, consistent with an evolutionary scenario in which bars dissolve into lenses. This scenario deserves further investigation through both theoretical and observational work.