Annotating biomedical images for supervised learning is a complex and labor-intensive task due to data diversity and its intricate nature. In this paper, we propose an innovative method, the efficient one-pass selective annotation (EPOSA), that significantly reduces the annotation burden while maintaining robust model performance. Our approach employs a variational autoencoder (VAE) to extract salient features from unannotated images, which are subsequently clustered using the DBSCAN algorithm. This process groups similar images together, forming distinct clusters. We then use a two-stage sample selection algorithm, called representative selection (RepSel), to form a selected dataset. The first stage is a Markov Chain Monte Carlo (MCMC) sampling technique to select representative samples from each cluster for annotations. This selection process is the second stage, which is guided by the principle of maximizing intra-cluster mutual information and minimizing inter-cluster mutual information. This ensures a diverse set of features for model training and minimizes outlier inclusion. The selected samples are used to train a VGG-16 network for image classification. Experimental results on the Med-MNIST dataset demonstrate that our proposed EPOSA outperforms random selection and other state-of-the-art methods under the same annotation budget, presenting a promising direction for efficient and effective annotation in medical image analysis.