We examine the changes in the properties of galactic bulges and discs with environment for a volume-limited sample of 12500 nearby galaxies from SDSS. We focus on galaxies with classical bulges. Classical bulges seem to have the same formation history as ellipticals of the same mass, and we test if environment determines whether or not a classical bulge possesses a disc. Using the projected fifth nearest neighbour density as a measure of local environment, we look for correlations with environment at fixed bulge stellar mass. In groups with fewer than 20 members, we find no evidence for changes in disc morphology with local density. At fixed bulge mass, disc mass and disc scale length are independent of local density. However, disc colour does increase (Delta(g - r) ~ 0.05 mag) as a function of local density in relatively poor groups. Therefore, the colour--density relation for classical bulge+disc galaxies in the field and in poor groups is due solely to changes in disc colour with density. In contrast, we find no correlations between disc colour and local density for classical bulge+disc galaxies in large, relaxed groups and clusters. However, there is a weak correlation between disc mass and group crossing time, suggesting morphological transformation takes places in rich groups. Our results add to the evidence that star formation is quenched in group environments, instead of clusters, and that star formation quenching and morphological transformation are separate processes. Overall, we show that environment has two effects on galactic discs: relatively low density environments can quench star formation in discs, while processes occurring in higher density environments contribute to the morphological transformation from disc-dominated systems to bulge-dominated systems.