The coronavirus disease 2019 (COVID-19) pandemic has caused an unprecedented health crisis for the global. Digital contact tracing, as a transmission intervention measure, has shown its effectiveness on pandemic control. Despite intensive research on digital contact tracing, existing solutions can hardly meet users requirements on privacy and convenience. In this paper, we propose BU-Trace, a novel permissionless mobile system for privacy-preserving intelligent contact tracing based on QR code and NFC technologies. First, a user study is conducted to investigate and quantify the user acceptance of a mobile contact tracing system. Second, a decentralized system is proposed to enable contact tracing while protecting user privacy. Third, an intelligent behavior detection algorithm is designed to ease the use of our system. We implement BU-Trace and conduct extensive experiments in several real-world scenarios. The experimental results show that BU-Trace achieves a privacy-preserving and intelligent mobile system for contact tracing without requesting location or other privacy-related permissions.