Bacterial poly-3-hydroxybutyrate is a thermoplastic biopolyester that is considered a potential alternative to traditional fossil-based plastics due to its rapid biodegradation performance in both soil and marine environments and its compostability. Due to problems in thermal and crystallization behaviors of the bacterial poly-3-hydroxybutyrate polymer, an improvement has been made in the cooling channel of the conventional fiber spinning process. Using an enhanced quench channel, named as a half tube on a conventional melt spinning line, melt spinning of the bacterial poly-3-hydroxybutyrate multifilament fibers is successfully carried out. The maximum crystallization temperature of polymers was taken into account while adjusting the quenching process. The study examined the impact of varying drawing ratios and the designed quenching apparatus on the thermal (differential scanning calorimetry), mechanical (tensile and drawing force tests), morphological, and crystal structure characteristics of fibers. The quenching apparatus has visibly created a homogeneous melt flow under the spinnerets. While it has a negative impact on fiber cross-sectional formation, raising the draw ratio greatly enhances mechanical properties.