The performances of machine translation (MT) systems are usually evaluated by the metric BLEU when the golden references are provided. However, in the case of model inference or production deployment, golden references are usually expensively available, such as human annotation with bilingual expertise. In order to address the issue of translation quality estimation (QE) without reference, we propose a general framework for automatic evaluation of the translation output for the QE task in the Conference on Statistical Machine Translation (WMT). We first build a conditional target language model with a novel bidirectional transformer, named neural bilingual expert model, which is pre-trained on large parallel corpora for feature extraction. For QE inference, the bilingual expert model can simultaneously produce the joint latent representation between the source and the translation, and real-valued measurements of possible erroneous tokens based on the prior knowledge learned from parallel data. Subsequently, the features will further be fed into a simple Bi-LSTM predictive model for quality estimation. The experimental results show that our approach achieves the state-of-the-art performance in most public available datasets of WMT 2017/2018 QE task.