BERT-based Neural Ranking Models (NRMs) can be classified according to how the query and document are encoded through BERT's self-attention layers - bi-encoder versus cross-encoder. Bi-encoder models are highly efficient because all the documents can be pre-processed before the query time, but their performance is inferior compared to cross-encoder models. Both models utilize a ranker that receives BERT representations as the input and generates a relevance score as the output. In this work, we propose a method where multi-teacher distillation is applied to a cross-encoder NRM and a bi-encoder NRM to produce a bi-encoder NRM with two rankers. The resulting student bi-encoder achieves an improved performance by simultaneously learning from a cross-encoder teacher and a bi-encoder teacher and also by combining relevance scores from the two rankers. We call this method TRMD (Two Rankers and Multi-teacher Distillation). In the experiments, TwinBERT and ColBERT are considered as baseline bi-encoders. When monoBERT is used as the cross-encoder teacher, together with either TwinBERT or ColBERT as the bi-encoder teacher, TRMD produces a student bi-encoder that performs better than the corresponding baseline bi-encoder. For P@20, the maximum improvement was 11.4%, and the average improvement was 6.8%. As an additional experiment, we considered producing cross-encoder students with TRMD, and found that it could also improve the cross-encoders.