Image classification has gained significant attention in recent years. However, the quantification of uncertainty in classification outcomes has only been more intensively studied in recent times. In this paper, we propose an equivariant bootstrap method, combined with an autoencoder, to quantify the inherent uncertainty of classification predictions. Specifically, the exact method involves applying group actions, such as rotations or translations, to the image. This process includes two applications of encoding, a single decoding step, and the application of the inverse of the group action, which generates a single bootstrap sample. Additionally, we introduce an inexact method that requires only a single pass through the encoder, trading off computational efficiency for slightly lower accuracy. We validate our methods through several numerical experiments, evaluating their performance using various metrics and benchmarking against other recent uncertainty quantification approaches. In particular, we focus on ablation studies that examine the impact of different group actions on the results.