To build ultimate dialogue agents, previous studies suggest models that ground both persona and knowledge. However, applying the dialogue system directly to the usual conversation is still limited because the system requires a complete sentence-formed persona and knowledge candidate sets from the given dataset. In contrast to the dialogue setting in the dataset, humans utilize semantic concepts in their minds rather than a set of pre-defined candidate sentences. Following this manner of human dialogue, we suggest an adaptive dialogue system that is applicable to situations where complete sentence-formed candidates are not given. Our model generates consistent and relevant persona descriptions and identifies relevant knowledge for engaging and knowledgeable responses, even with fragmentary information. We show that our model outperforms previous baselines that utilize persona and knowledge candidate sentences and conduct the human evaluation on the machine-generated responses. In addition, we conduct ablation studies to demonstrate the effectiveness of each component of our model. Furthermore, we apply our model to other dialogue datasets that only ground knowledge or persona to showcase its adaptability. Our code is available at https://github.com/dlawjddn803/BeCand.