Understanding the mechanisms of the cellular aging processes is crucial for attempting to extend organismal lifespan and for studying age-related degenerative diseases. Yeast cells divide through budding, providing a classical biological model for studying cellular aging. With their powerful genetics, relatively short cell cycle, and well-established signaling pathways also found in animals, yeast cells offer valuable insights into the aging process. Recent experiments suggested the existence of two aging modes in yeast characterized by nucleolar and mitochondrial declines, respectively. By analyzing experimental data, this study shows that cells evolving into those two aging modes behave differently when they are young. While buds grow linearly in both modes, cells that consistently generate spherical buds throughout their lifespan demonstrate greater efficacy in controlling bud size and growth rate at young ages. A three-dimensional multiscale chemical-mechanical model was developed and used to suggest and test hypothesized impacts of aging on bud morphogenesis. Experimentally calibrated model simulations showed that during the early stage of budding, tubular bud shape in one aging mode could be generated by locally inserting new materials at the bud tip, a process guided by the polarized Cdc42 signal. Furthermore, the aspect ratio of the tubular bud could be stabilized during the late stage as observed in experiments in this work. The model simulation results suggest that the localization of new cell surface material insertion, regulated by chemical signal polarization, could be weakened due to cellular aging in yeast and other cell types, leading to the change and stabilization of the bud aspect ratio.