The early pioneering Neural Architecture Search (NAS) works were multi-trial methods applicable to any general search space. The subsequent works took advantage of the early findings and developed weight-sharing methods that assume a structured search space typically with pre-fixed hyperparameters. Despite the amazing computational efficiency of the weight-sharing NAS algorithms, it is becoming apparent that multi-trial NAS algorithms are also needed for identifying very high-performance architectures, especially when exploring a general search space. In this work, we carefully review the latest multi-trial NAS algorithms and identify the key strategies including Evolutionary Algorithm (EA), Bayesian Optimization (BO), diversification, input and output transformations, and lower fidelity estimation. To accommodate the key strategies into a single framework, we develop B2EA that is a surrogate assisted EA with two BO surrogate models and a mutation step in between. To show that B2EA is robust and efficient, we evaluate three performance metrics over 14 benchmarks with general and cell-based search spaces. Comparisons with state-of-the-art multi-trial algorithms reveal that B2EA is robust and efficient over the 14 benchmarks for three difficulty levels of target performance. The B2EA code is publicly available at \url{https://github.com/snu-adsl/BBEA}.