We combine new Herschel/SPIRE sub-millimeter observations with existing multiwavelength data to investigate the dust scaling relations of the Herschel Reference Survey, a magnitude-, volume-limited sample of ∼300 nearby galaxies in different environments. We show that the dust-to-stellar mass ratio anti-correlates with stellar mass, stellar mass surface density and NUV-r colour across the whole range of parameters covered by our sample. Moreover, the dust-to-stellar mass ratio decreases significantly when moving from late-to early-type galaxies. These scaling relations are similar to those observed for the Hi gas-fraction, supporting the idea that the cold dust is tightly coupled to the cold atomic gas component in the interstellar medium. We also find a weak increase of the dust-to-Hi mass ratio with stellar mass and colour but no trend is seen with stellar mass surface density. By comparing galaxies in different environments we show that, although these scaling relations are followed by both cluster and field galaxies, Hi-deficient systems have, at fixed stellar mass, stellar mass surface density and morphological type systematically lower dust-to-stellar mass and higher dust-to-Hi mass ratios than Hi-normal/field galaxies. This provides clear evidence that dust is removed from the star-forming disk of cluster galaxies but the effect of the environment is less strong than what is observed in the case of the Hi disk. Such effects naturally arise if the dust disk is less extended than the Hi and follows more closely the distribution of the molecular gas phase, i.e., if the dust-to-atomic gas ratio monotonically decreases with distance from the galactic center. © 2012 ESO.