This work provides the first direct evidence that the puzzling dielectric Debye process observed in mono-alcohols is coupled to density fluctuations. The results open up for an explanation of the Debye process within the framework of conventional liquid-state theory. The spectral shape of the dynamical bulk modulus of the two studied mono-alcohols, 2-ethyl-1-hexanol and 4-methyl-3-heptanol, is nearly identical to that of their corresponding shear modulus, and thus the supramolecular structures believed to be responsible for the slow dielectric Debye process are manifested in the bulk modulus in the same way as in the shear modulus.