We address the optimal quantizer design problem for distributed Bayesian parameter estimation where each sensor quantizes its local observation into one bit and transmit it through non-ideal channels to the Fusion Center. We first develop an asymptotic performance limit (PL) as a performance bound for any quantizer design with a known prior. Aided by this PL, we derive the optimal quantizer and near optimal quantizer with set of observation models that achieves the PL, thus solve a set of optimal quantizer design problem for distributed estimation.