With the enrichment of smartphones, driving distractions caused by phone usages have become a threat to driving safety. A promising way to mitigate driving distractions is to detect them and give real-time safety warnings. However, existing detection algorithms face two major challenges, low user acceptance caused by in-vehicle camera sensors, and uncertain accuracy of pre-trained models due to drivers individual differences. Therefore, this study proposes a domain-specific automated machine learning (AutoML) to self-learn the optimal models to detect distraction based on lane-keeping performance data. The AutoML integrates the key modeling steps into an auto-optimizable pipeline, including knowledge-based feature extraction, feature selection by recursive feature elimination (RFE), algorithm selection, and hyperparameter auto-tuning by Bayesian optimization. An AutoML method based on XGBoost, termed AutoGBM, is built as the classifier for prediction and feature ranking. The model is tested based on driving simulator experiments of three driving distractions caused by phone usage: browsing short messages, browsing long messages, and answering a phone call. The proposed AutoGBM method is found to be reliable and promising to predict phone-related driving distractions, which achieves satisfactory results prediction, with a predictive power of 80\% on group level and 90\% on individual level accuracy. Moreover, the results also evoke the fact that each distraction types and drivers require different optimized hyperparameters values, which reconfirm the necessity of utilizing AutoML to detect driving distractions. The purposed AutoGBM not only produces better performance with fewer features; but also provides data-driven insights about system design.