Understanding bond (debt) valuation and predicting future prices are of great importance in finance. Bonds are a major source of long-term capital in U.S. financial markets along with stocks. However, compared with stocks, bonds are understudied. One main reason is the infrequent trading in the secondary market, which results in irregular intervals and missing observations. This paper attempts to overcome this challenge by leveraging network information from bond-fund holding data and proposes a novel method to predict bond prices (yields). We design the temporal bipartite graph neural networks (TBGNN) with self-supervision regularization that entails multiple components: the bipartite graph representation module of learning node embeddings from the bond and fund interactions and their associated factors; the recurrent neural network module to model the temporal interactions; and the self-supervised objective to regularize the unlabeled node representation with graph structure. The model adopts a minibatch training process (Minibatch Stochastic Gradient Descent) in a deep learning platform to alleviate the model complexity and computation cost in optimizing different modules and objectives. Results show that our TBGNN model provides a more accurate prediction of bond price and yield. It outperforms multiple existing graph neural networks and multivariate time series methods: improving R2 by 6%-51% in bond price prediction and 5%-70% in bond yield prediction.