We examine the network of bilateral trading relations between insurers and dealers in the over-the-counter corporate bond market. Using comprehensive regulatory data we find that many insurers use only one dealer while the largest insurers have a network of up to eighty dealers. To understand the heterogeneity in network size we build a model of decentralized trade in which insurers trade off the benefits of repeat business against more intense dealer competition. Empirically, large insurers form more relations and receive better prices than small insurers. The model matches both the distribution of insurers network sizes and how prices depend on insurers size and the size of their dealer network.