By incorporating additional contextual information, deep biasing methods have emerged as a promising solution for speech recognition of personalized words. However, for real-world voice assistants, always biasing on personalized words with high prediction scores can degrade the performance of recognizing common words. To address this issue, we propose an adaptive contextual biasing method based on Context-Aware Transformer Transducer (CATT) that utilizes the biased encoder and predictor embeddings to perform streaming prediction of contextual phrase occurrences. This prediction is then used to switch the bias list on and off, enabling the model to adapt to both personalized and common scenarios. Experiments on Librispeech and internal voice assistant datasets show that our approach can achieve up to 6.7% and 20.7% relative reduction in WER and CER compared to the baseline respectively, mitigating up to 96.7% and 84.9% of the relative WER and CER increase for common cases.