A two-user Gaussian broadcast channel (GBC) with finite input constellations is addressed in this paper. The constellation-constrained capacity region for the two-user GBC by recently proposed bit-division multiplexing (BDM) is derived. BDM can be seen as a practical implementation of constellation-constrained nonlinear superposition coding (SC). For comparison, the constellation-constrained capacity region for the two-user GBC by traditional constellation-constrained linear SC is also computed. With similar implementation complexity, BDM outperforms traditional constellation-constrained linear SC with lower shaping loss in the capacity defined in this paper. Analytical results show that the upper boundary of the capacity region for the two-user GBC can be well approached by BDM with amplitude phase-shift keying modulation, which could be considered as the preliminary demonstration on the applicability of BDM in practical systems.