In the transmission of hyperspectral images that have been compressed using absolute moment block truncation coding (AMBTC), confidentiality and security of crucial information is often a concern. Although many data hiding (DH) methods based on AMBTC work well in guaranteeing a large amount of secret information can be embedded, the requirements of actual user scenarios, such as reversibility and imperceptibility, are degraded sometimes. To address these challenges, we propose an embedding pattern that utilizes bitmap prediction to embed secret information within the bitmaps while preserving the standard format of AMBTC codes and enabling recovery of the cover image without loss. Our proposed method, therefore, belongs to the category of reversible data hiding (RDH) techniques. Since the embedding distortion (ED) reduction is an essential object, an adaptive embedding order based on the features of AMBTC codes is conducted. Furthermore, we propose a dynamical embedding scheme to reduce ED when we are striving to achieve a larger embedding capacity (EC).