The criteria for occurrence and the dynamical features of electrostatic solitary waves in a homogeneous, unmagnetized ultra dense plasma penetrated by a negative ion beam are investigated, relying on a quantum hydrodynamic model. The ionic components are modeled as inertial fluids, while the relativistic electrons obey Fermi-Dirac statistics. A new set of exact analytical conditions for localized solitary pulses to exist is obtained, in terms of plasma density. The algebraic analysis reveals that these depend sensitively on the negative ion beam characteristics,that is, the beam velocity and density. Particular attention is paid to the simultaneous occurrence of positive and negative potential pulses, identified by their respective distinct am bipolar electric field structure forms. It is shown that the coexistence of positive and negative potential pulses occurs in a certain interval of parameter values, where the ion beam inertia becomes significant.