Using ordinary Portland cement (OPC) in concrete has significant environmental and sustainability concerns. Notably, in the production of OPC, large volumes of greenhouse gases are produced, which contribute to global warming, and large amounts of natural raw materials are used, which can lead to the depletion of nonrenewable resources with time. In addition, OPC production is highly energy-intensive. To mitigate these concerns, it has become common practice to reduce the amount of OPC used in concrete production by partially replacing OPC with a supplementary cementitious material (SCM). Most of the SCMs used have pozzolanic properties and react with free lime in OPC to provide more cementitious material, which increases the long-term strength of concrete and also densifies the pore structure, resulting in improved durability in harsh environments. This study explored the effect of OPC on the resistance to sulfuric acid attack and drying shrinkage when OPC is partially replaced by processed bagasse ash (PBA) at dosages of up to 50%, together with 5% silica fume. Both materials are pozzolanic and are expected to react with free lime in OPC concrete to increase the strength and densify the concrete; however, with increased PBA dosage, the cement is diluted, and a reduction in strength can be expected. This study explores the benefits that can be realized, focusing primarily on sulfuric acid resistance and the reduction of drying shrinkage.