The growing number of multi-relational networks pose new challenges concerning the development of methods for solving classical graph problems in a multi-layer framework, such as link prediction. In this work, we combine an existing bipartite local models method with approaches for link prediction from communities to address the link prediction problem in multi-layer graphs. To this end, we extend existing community detection-based link prediction measures to the bipartite multi-layer network setting. We obtain a new generic framework for link prediction in bipartite multi-layer graphs, which can integrate any community detection approach, is capable of handling an arbitrary number of networks, rather inexpensive (depending on the community detection technique), and able to automatically tune its parameters. We test our framework using two of the most common community detection methods, the Louvain algorithm and spectral partitioning, which can be easily applied to bipartite multi-layer graphs. We evaluate our approach on benchmark data sets for solving a common drug-target interaction prediction task in computational drug design and demonstrate experimentally that our approach is competitive with the state-of-the-art.