Deep biasing (DB) enhances the performance of end-to-end automatic speech recognition (E2E-ASR) models for rare words or contextual phrases using a bias list. However, most existing methods treat bias phrases as sequences of subwords in a predefined static vocabulary. This naive sequence decomposition produces unnatural token patterns, significantly lowering their occurrence probability. More advanced techniques address this problem by expanding the vocabulary with additional modules, including the external language model shallow fusion or rescoring. However, they result in increasing the workload due to the additional modules. This paper proposes a dynamic vocabulary where bias tokens can be added during inference. Each entry in a bias list is represented as a single token, unlike a sequence of existing subword tokens. This approach eliminates the need to learn subword dependencies within the bias phrases. This method is easily applied to various architectures because it only expands the embedding and output layers in common E2E-ASR architectures. Experimental results demonstrate that the proposed method improves the bias phrase WER on English and Japanese datasets by 3.1 -- 4.9 points compared with the conventional DB method.