  We explore the collective electronic excitations of bilayer molybdenum
disulfide (MoS$_2$) using the density functional theory together with the
random phase approximation. The many-body dielectric function and electron
energy-loss spectra are calculated using an {\it ab initio} based model
involving material-realistic physical properties. The electron energy-loss
function of bilayer MoS$_2$ system is found to be sensitive to either electron
or hole doping and it is owing to the fact that the Kohn-Sham band dispersions
are not symmetric for energies above and below the zero Fermi level. Three
plasmon modes are predicted. A damped high-energy mode, one optical mode
(in-phase mode) for which the plasmon dispersion exhibits $\sqrt q $ in the
long wavelength limit originating from low-energy electron scattering and
finally a highly damped acoustic mode (out-of-phase mode).
