In this work we provide a first-principles description of the electronic and optical properties of bilayers C3N, with different stacking motifs AB, AB', and AA'. Starting from quasiparticle electronic band structures, we solve the Bethe-Salpeter equation (BSE) to access the excitonic properties of these bilayers. For all stacking sequences, we see strong optical absorption at energies lower than but close to that of the monolayer. Most relevant, we predict a strong quenching of the low-energy optical absorption, with negligible oscillator strengths of low-lying bound excitons.