Penaeus monodon (tiger shrimp), Metapenaeus monoceros (brown shrimp), and Fenneropenaeus indicus (white shrimp) are the most economically important shrimp species in the waters of the Bay of Bengal, Bangladesh. This is the first analytical study to assess three major shrimp stocks using both length-based and catch-based methods, such as length-based Bayesian biomass estimation (LBB), length-based indicator (LBI), and a catch-based method entitled JABBA (Just Another Bayesian Biomass Assessment), to explore and process the data; estimate the growth parameters, with length at first capture; present relative biomasses; and approximate the reference points. The parameters of the von Bertalanffy Growth Function (VBGF) analysis for the tiger, brown, and white shrimps were L∞ = 113.0 mm, 85.4 mm, and 76.4 mm, respectively, for carapace length. Our results showed that the relative biomass level (B/BMSY) of the tiger shrimp was 0.43, suggesting an overfished status, and brown and white shrimps were 0.84 and 0.96, indicating that they were fully exploited but not overfished. This study, therefore, advised an optimum carapace length limit to catch from 57.0–70.0 mm for tiger shrimp, 44.0–53.0 mm for brown shrimp, and 40.0–48.0 mm for white shrimp. The estimated maximum sustainable yield (MSY) reference points were as follows: optimal biomass BMSY = 3116 mt, 15,885 mt, and 2649 mt for tiger, brown, and white shrimp, respectively, and optimal harvest rate uMSY = 12%, 33%, and 8% for tiger, brown, and white shrimp, respectively. The average annual catch values for the last ten years were 265 mt, 2396 mt, and 115 mt below the estimated MSY values of 389 mt, 4899 mt, and 209 mt for tiger, brown, and white shrimp, respectively. But, brown shrimp had the estimated highest carrying capacity (31,770 mt) and intrinsic growth rate (0.66) than the tiger and white shrimp, which was replicated distinctly in the graphical representation of the Kobe plot and the surplus production plot. Hence, the brown shrimp stock is estimated to be in a better state than the tiger and white shrimp stocks.