As an output-to-output dynamical representation of engineering structures, the transmissibility function (TF) has been widely reported to be a damage-sensitive but excitation-insensitive damage feature. However, most TF-based novelty detection approaches fail to accommodate various uncertainties with a proper probabilistic model. Making full use of the complex Gaussian ratio probabilistic model of raw scalar TFs, a data-driven structural novelty detection technology is proposed by integrating the closed-form approximation of the Bhattacharyya distance of TFs and the Bayesian resampling scheme. A closed-form approximation of the Bhattacharyya distance is efficiently derived by applying the Laplace method of asymptotic expansion to provide a probabilistic metric of the dissimilarity between distributions of TFs under different states without resorting to time-consuming numerical integration. A Bayesian resampling scheme is adopted to accommodate the variability of the statistical parameters involved in the probabilistic model of TFs. Based on the Laplace asymptotic expansion of the Bhattacharyya distance and Bayesian resampling scheme, two state discrimination techniques including Gaussian mixture model (GMM) clustering method and threshold method are utilized to detect the existence of damage. Two case studies, including a laboratory model test as well as a field test of a bridge, are carried out to verify the accuracy and efficiency of the proposed algorithm. The results demonstrate that, compared with the Mahalanobis distance-based method with the implicit assumption of Gaussian distribution for TFs, the Bhattacharyya distance-driven algorithm can achieve better performance and robustness due to properly considering the deviations in TFs not following the Gaussian distribution.