Almond bagasse resulting after the production of almond-based drinks represents a promising by-product with potential for use as a functional ingredient. To facilitate its utilization, the stability of this material can be achieved through dehydration processes such as hot air drying or freeze-drying. Nevertheless, owing to its high fat content, almond bagasse is prone to lipid oxidation, which could result in undesirable quality. Therefore, the objective of this work was to assess the impact of dehydration (by hot air drying at 60 and 70 °C and by freeze-drying) and storage (at room temperature and in accelerated conditions) on the functional quality and stability of almond bagasse powder. Throughout the dehydration process, it was observed that antioxidant compounds were preserved without significant differences among dehydration treatments. These compounds increased over the storage period, especially in the samples treated with hot air. Regarding antiradical capacity, the hot-air-dried samples showed higher values than the freeze-dried ones, although in all cases, it increased during storage. For total phenols in samples air-dried at 70 °C, increases of more than 50% were observed. The acidity and peroxide index were increased in the extended storage period, although they did not reach critical values. Samples stored for 180 days showed peroxide values ranging from 10 to 12.8 meq O2/kg dry matter for samples stored at room temperature and from 14.7 to 23 meq O2/kg dry matter for samples subjected to accelerated storage.