Chemical potentials of charged hard-dumbbell fluids are obtained by Monte Carlo simulations using Widom's test-particle method, corresponding compressibility factors are achieved by integration of chemical potentials at different densities. A molecular thermodynamic model is also developed for these charged hard-dumbbell fluids where the residual Helmholtz function is composed of two terms: a reference term responsible for the charged hard spheres and a bonding contribution measuring the sticky interactions between positive and negative hard ions. Model predictions are in good agreement with simulation results.