The Bogoliubov–de Gennes (BdG) type equations are derived for the Coulomb Bose gas describing the electrodynamics of charged bosons. The gauge invariant dielectric response function and collective excitations of a charged Bose gas at T=0 are found. We find a plasmon branch which is the same as the single-particle Bogoliubov spectrum in agreement with the textbook result. The superconducting properties of the charged Bose gas are verified. A gauge-invariant formalism for calculating the response of the supracondensate particles is proposed.