Optimal Power Flow (OPF) plays a crucial role in optimization and operation of the bipolar DC distribution network (Bi-DCDN). However, existing OPF models encounter difficulties in the power optimization of Bi-DCDNs due to the optimal power expressed as a product form, i.e., the product of voltage and current. Hence, this brief formulates the OPF problem of Bi-DCDNs using the branch flow model (BFM). The BFM employs power, instead of current, to account for the unique structure of Bi-DCDNs. Convex relaxation and linear approximation are sequentially applied to reformulate the BFM-based OPF, presenting it as a second-order cone programming (SOCP) problem. Further, the effectiveness of the proposed OPF model is verified in case studies. The numerical results demonstrate that the BFM-based OPF is a feasible and promising approach for Bi-DCDNs.