This paper proposes a new methodology to address the image quality problem encountered as the use of an unmanned aerial vehicle (UAV) in the field of bridge inspection increased. When inspecting a bridge, the image obtained from the UAV was degraded by various interference factors such as vibration, wind, and motion of UAV. Image quality degradation such as blur, noise, and low-resolution is a major obstacle in utilizing bridge inspection technology based on UAV. In particular, in the field of bridge inspection where damages must be accurately and quickly detected based on data obtained from UAV, these quality issues weaken the advantage of using UAVs by requiring re-take of images through re-flighting. Therefore, in this study, image quality assessment (IQA) based on local blur map (LBM) and image quality enhancement (IQE) using the variational Dirichlet (VD) kernel estimation were proposed as a solution to address the quality issues. First, image data was collected by setting different camera parameters for each bridge member. Second, a blur map was generated through discrete wavelet transform (DWT) and a new quality metric to measure the degree of blurriness was proposed. Third, for low-quality images with a large degree of blurriness, the blind kernel estimation and blind image deconvolution were performed to enhance the quality of images. In the validation tests, the proposed quality metric was applied to material image sets of bridge pier and deck taken from UAV, and its results were compared with those of other quality metrics based on singular value decomposition (SVD), sum of gray-intensity variance (SGV) and high-frequency multiscale fusion and sort transform (HiFST) methods. It was validated that the proposed IQA metric showed better classification performance on UAV images for bridge inspection through comparison with the classification results by human perception. In addition, by performing IQE, on average, 26% of blur was reduced, and the images with enhanced quality showed better damage detection performance through the deep learning model (i.e., mask and region-based convolutional neural network).