Recently, there has been significant interest in bio-based degradable plastics owing to their potential as a green and sustainable alternative to synthetic plastics due to their biodegradable properties. Polyhydroxybutyrate (PHB) is a biodegradable polymer that is produced by bacteria and archaea as carbon and energy reserves. Due to its rapid degradation in natural environments, it can be considered a biodegradable plastic alternative. In the present study, a dye-based procedure was used to screen PHB-producing bacteria isolated from mangrove soil samples. Among the seven isolates, Agromyces indicus (A. indicus), identified by means of 16S rRNA analysis, accumulated the highest amount of PHB. The extracted polymer was characterized by a UV–Vis spectrophotometer, Fourier-transform infrared (FTIR) spectroscopy, and for the presence of the phbB gene, which confirmed the structure of the polymer as PHB. The maximum PHB production by A. indicus was achieved after 96 h of incubation at a pH of 8.0 and 35 °C in the presence of 2% NaCl, with glucose and peptone as the carbon and nitrogen sources, respectively. The strain was found to be capable of accumulating PHB when various cheap agricultural wastes, such as rice, barley, corn, and wheat bran, were used as the carbon sources. The response surface methodology (RSM) through the central composite design (CCD) for optimizing the PHB synthesis was found to be highly efficient at augmenting the polymer yields. As a result of the optimum conditions obtained from the RSM, this strain can increase the PHB content by approximately 1.4-fold when compared with an unoptimized medium, which would substantially lower the production cost. Therefore, the isolate A. indicus strain B2 may be regarded as one of the best candidates for the industrial production of PHB from agricultural wastes, and it can remove the environmental concerns associated with synthetic plastic.