Privacy preservation remains a key challenge in data mining and Natural Language Understanding (NLU). Previous research shows that the input text or even text embeddings can leak private information. This concern motivates our research on effective privacy preservation approaches for pretrained Language Models (LMs). We investigate the privacy and utility implications of applying dχ-privacy, a variant of Local Differential Privacy, to BERT fine-tuning in NLU applications. More importantly, we further propose privacy-adaptive LM pretraining methods and show that our approach can boost the utility of BERT dramatically while retaining the same level of privacy protection. We also quantify the level of privacy preservation and provide guidance on privacy configuration. Our experiments and findings lay the groundwork for future explorations of privacy-preserving NLU with pretrained LMs.