We report a cathodoluminescence (CL) study of layered germanium sulfide (GeS) where we observe a sharp emission peak from flakes covered with a thin hexagonal boron nitride film. GeS is a material that has recently attracted considerable interest due to its emission in the visible region and its strong anisotropy. The measured CL peak is at ~1.69 eV for samples ranging in thickness from 97 nm to 45 nm, where quantum-confinement effects can be excluded. By performing ab initio ground- and excited-state simulations for the bulk compound, we show that the measured optical peak can be unambiguously explained by radiative recombination of the first free bright bound exciton, which is due to a mixing of direct transitions near the Γ-point of the Brillouin Zone and it is associated to a very large optical anisotropy. The analysis of the corresponding excitonic wave function shows a Wannier-Mott interlayer character, being spread not only in-plane but also out-of-plane.