A series of newly synthesized mono-5-isoxazolidine and bis(5-isoxazolidine) derivatives were obtained as bicyclic cycloadducts. These compounds were rationally designed and constructed through a 1,3-dipolar cycloaddition between nitrones and 3,9-divinyl-2,4,8,10-tetraoxaspiro(5.5)undecane, with the goal of discovering new antimicrobial and antioxidant agents. The resulting isoxazolidines were thoroughly characterized using FT-IR, ¹³C-NMR, and ¹H-NMR spectroscopic techniques. The physicochemical properties—including lipophilicity and predicted bioactivity scores—were evaluated using computational methods. Pharmacokinetic parameters, such as absorption, distribution, metabolism, and excretion (ADME), were also predicted in silico. Biological screening demonstrated that many of the synthesized compounds possess notable antimicrobial activity against a range of bacterial strains, including the Gram-negative species Pseudomonas aeruginosa and Escherichia coli, as well as the Gram-positive species Streptococcus pyogenes and Staphylococcus aureus. Several compounds also exhibited antifungal activity against Candida albicans, Aspergillus niger, and Aspergillus clavatus. In many cases, the compounds performed better than standard reference drugs. Antioxidant evaluation at different concentrations revealed that selected cycloadducts displayed strong, moderate, or weak radical-scavenging properties. Molecular docking studies further supported the biological findings, showing that the synthesized molecules bind effectively—often more favorably than the standard drug—to the active site of pantothenate synthetase (PDB ID: 2X3F).