The personalized bundle generation problem, which aims to create a preferred bundle for user from numerous candidate items, receives increasing attention in recommendation. However, existing works ignore the order-invariant nature of the bundle and adopt sequential modeling methods as the solution, which might introduce inductive bias and cause a large latency in prediction. To address this problem, we propose to perform the bundle generation via non-autoregressive mechanism and design a novel encoder-decoder framework named BundleNAT, which can effectively output the targeted bundle in one-shot without relying on any inherent order. In detail, instead of learning sequential dependency, we propose to adopt pre-training techniques and graph neural network to fully embed user-based preference and item-based compatibility information, and use a self-attention based encoder to further extract global dependency pattern. We then design a permutation-equivariant decoding architecture that is able to directly output the desired bundle in a one-shot manner. Experiments on three real-world datasets from Youshu and Netease show the proposed BundleNAT significantly outperforms the current state-of-the-art methods in average by up to 35.92%, 10.97% and 23.67% absolute improvements in Precision, Precision+, and Recall, respectively.