Biomedical entity linking is the task of identifying mentions of biomedical concepts in text documents and mapping them to canonical entities in a target thesaurus. Recent advancements in entity linking using BERT-based models follow a retrieve and rerank paradigm, where the candidate entities are first selected using a retriever model, and then the retrieved candidates are ranked by a reranker model. While this paradigm produces state-of-the-art results, they are slow both at training and test time as they can process only one mention at a time. To mitigate these issues, we propose a BERT-based dual encoder model that resolves multiple mentions in a document in one shot. We show that our proposed model is multiple times faster than existing BERT-based models while being competitive in accuracy for biomedical entity linking. Additionally, we modify our dual encoder model for end-to-end biomedical entity linking that performs both mention span detection and entity disambiguation and out-performs two recently proposed models.