Bundle recommendation is an emerging research direction in the recommender system with the focus on recommending customized bundles of items for users. Although Graph Neural Networks (GNNs) have been applied to this problem and achieved superior performance, existing methods underexplore the graph-level GNN methods, which exhibit great potential in traditional recommender system. Furthermore, they usually lack the transferability from one domain with sufficient supervision to another domain which might suffer from the label scarcity issue. In this work, we propose a subgraph-based Graph Neural Network model, SuGeR, for bundle recommendation to handle these limitations. SuGeR generates heterogeneous subgraphs around the user-bundle pairs and then maps those subgraphs to the users' preference predictions via neural relational graph propagation. Experimental results show that SUGER significantly outperforms the state-of-the-art baselines in the basic and the transfer bundle recommendation tasks by up to 77.17% by NDCG@40. The source code is available at: https://github.com/Zhang-Zhenning/SUGER.