Expansive soils present continuing challenges in geotechnical construction due to their high plasticity and significant swelling potential, which often cause differential settlement and structural damage in foundations and pavements. This study examines the stabilization of expansive soils using a dry geopolymer binder combined with bagasse ash, an agro-industrial by-product rich in amorphous silica with strong pozzolanic activity, as a sustainable, low-carbon alternative to conventional lime- or cement-based stabilizers. Geopolymer-to-bagasse-ash ratios of 1:5, 2:3, 3:2, and 5:1 were evaluated through Atterberg limits, differential free swell, and standard Proctor compaction tests to identify the optimum stabilization dosage. The optimum ratio, a geopolymer-to-bagasse-ash proportion of 3:2, reduced the plasticity index from 40.75% to 23.53% and the swell index from 110.04% to 9.33%, demonstrating substantial improvement in soil workability and volumetric stability. Unconfined compressive strength (UCS) testing at this optimum dosage showed an increase from approximately 82 kPa in untreated soil to 532 kPa, indicating a significant gain in load-bearing capacity suitable for subgrade and foundation applications. Durability was further assessed through wetting–drying cycles by measuring strength retention and mass loss under repeated exposure, while ultrasonic pulse velocity (UPV) testing provided a non-destructive method to monitor internal soil–matrix integrity and curing development over time. Scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDX) analyses were used to characterize microstructural changes and elemental composition, confirming the formation of repolymerization and pozzolanic reaction products responsible for the observed strength improvements and enhanced durability. Overall, the results show that dry geopolymer–bagasse ash stabilization is a durable, sustainable, and economically viable alternative to conventional binders, with strong potential for subgrade and foundation stabilization while also addressing bagasse ash disposal issues in the sugar industry.