Proliferating bacterial cells exhibit stochastic growth and shape dynamics but the regulation of noise in bacterial growth and morphogenesis remains poorly understood. A quantitative understanding of morphogenetic noise control, and how it changes under different growth conditions, would provide better insights into cell-to-cell variability and intergenerational fluctuations in cell physiology. Using multigenerational growth and shape data of single Escherichia coli and Caulobacter crescentus cells, we deduce the equations governing growth and shape dynamics of bacterial cells. Interestingly, we find that both E. coli and C. crescentus cells grow faster than an exponential within a cell cycle, irrespective of nutrient or temperature conditions. We propose a mechanistic model that explains the emergence of super-exponential growth from autocatalytic production of ribosomes, coupled to the rate of cell elongation and surface area synthesis. Using this new model and statistical inference on large datasets, we construct the Langevin equations governing cell size and shape dynamics of E. coli cells in different growth conditions. The single-cell level model predicts how noise in intragenerational and intergenerational processes regulate variability in cell morphology and generation times, revealing quantitative strategies for cellular resource allocation and morphogenetic noise control in different growth conditions.