Understanding how bulges and disks grow across cosmic time is key to uncovering the physical processes that shape galaxy evolution. We investigate the wavelength-dependent structural evolution of galaxies using a mass-complete sample of 44,000 star-forming galaxies (SFGs) and 34,000 quiescent galaxies (QGs) at z<0.85. By modelling bulges and disks separately in rest-frame UV (3000 Å) and optical (5000 Å) images from the CFHT CLAUDS and Subaru HSC-SSP surveys, we present the first systematic analysis of the size–mass relation (SMR) for individual galaxy components across two rest-frame wavelengths. For both SFGs and QGs, disks of Milky-Way mass-galaxies are significantly larger than their bulges, with the contrast being more pronounced in the UV. At fixed galaxy type, both bulges and disks are, on average, larger in SFGs than in QGs. Component sizes show strong wavelength dependence: disks are larger in the UV, while bulges are slightly more compact in the UV. We further find that bulge sizes grow more rapidly with mass than disk sizes, and that the growth rates differ across wavelengths. These results support a scenario in which bulge expansion dominates the structural evolution of SFGs, while the buildup of QGs is driven by recently quenched arrivals and minor mergers.