We present a new measurement of the inclusive forward-backward production asymmetry and its rapidity and mass dependence. The measurements are performed with data corresponding to an integrated luminosity of of collisions at , recorded with the CDF-II Detector at the Fermilab Tevatron. Significant inclusive asymmetries are observed in both the laboratory frame and the rest frame, and in both cases are found to be consistent with conservation under interchange of and . In the rest frame, the asymmetry is observed to increase with the rapidity difference, , and with <?format ?>the invariant mass of the system. Fully corrected parton-level asymmetries are derived in two regions of each variable, and the asymmetry is found to be most significant at large and . For , the parton-level asymmetry in the rest frame is compared to a next-to-leading order QCD prediction of .