The Predictor-Estimator framework for quality estimation (QE) is commonly used for its strong performance. Where the predictor and estimator works on feature extraction and quality evaluation, respectively. However, training the predictor from scratch is computationally expensive. In this paper, we propose an efficient transfer learning framework to transfer knowledge from NMT dataset into QE models. A Predictor-Estimator alike model named BAL-QE is also proposed, aiming to extract high quality features with pre-trained NMT model, and make classification with a fine-tuned Bottleneck Adapter Layer (BAL). The experiment shows that BAL-QE achieves 97% of the SOTA performance in WMT19 En-De and En-Ru QE tasks by only training 3% of parameters within 4 hours on 4 Titan XP GPUs. Compared with the commonly used NuQE baseline, BAL-QE achieves 47% (En-Ru) and 75% (En-De) of performance promotions.