In this article we report a novel analytic solution describing a cosmological model with a matter content represented by a one dissipative fluid component, in the framework of the causal Israel-Stewart theory. The dissipative fluid is described by a barotropic equation of state p = (gamma - 1)rho and the bulk viscosity has been assumed of the form xi = xi 0 rho(s). We study within the parameter space which label the solution, a suited region compatible with an accelerated expansion of the universe for late times, as well as stability properties of the solution at the critical parameter value gamma = 1 and for s = 1/2. We study as well the consequences that arise from the positiveness of the entropy production along the time evolution. We found that the solution for pressureless dark matter, gamma = 1, can well describe a universe with a transition from a decelerated expansion to an accelerated one at late times, but with a very large non-adiabatic contribution to speed of sound. Finally, the kinematics and thermodynamics properties of the solutions are discussed in terms of the type of expansion and entropy production.