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The reconfiguration of wireless channels with reconfigurable reflecting surface (RIS) technology offers new design options for future wireless networks. Due to its high altitude and increased probability of establishing line-of-sight linkages with ground source/destination nodes, aerial RIS (ARIS) has greater deployment flexibility than traditional terrestrial RIS. It also provides a wider-view signal reflection. To leverage the advantages of ARIS-enabled systems, this paper defines air-to-ground linkages via Nakagami-m small-scale fading and inverse-Gamma large-scale shadowing, considering realistic composite fading channels. To construct a tight approximate closed-form formula for the outage probability (OP), a new mathematical framework is proposed. Additionally, a deep-learning-based system called the BiLSTM model is deployed to evaluate OP performance in the 3D spatial movement of the ARIS system. In the offline phase, the proposed model is trained with real-value channel state estimation sets and enhances OP performance in the online phase by learning channel information in a bidirectional manner. Simulation results demonstrate that the proposed BiLSTM model outperforms all other models in analyzing OP for the ARIS system.