The purpose of this study was to measure the strength of various bamboo fibres and their epoxy composites based on the bamboo ages and harvesting seasons. Three representative samples of 1–3-year-old bamboo plants were collected in November and February. Bamboo fibres and their epoxy composites had the highest tensile strength and Young’s modulus at 2 years old and in November. The back-calculated tensile strengths using the “rule of mixture” of Injibara, Kombolcha, and Mekaneselam bamboo-fibre-reinforced epoxy composites were 548 ± 40–422 ± 33 MPa, 496 ± 16–339 ± 30 MPa, and 541 ± 21–399 ± 55 MPa, whereas the back-calculated Young’s moduli using the “rule of mixture” were 48 ± 5–37 ± 3 GPa, 36 ± 4–25 ± 3 GPa, and 44 ± 2–40 ± 2 GPa, respectively. The tensile strengths of the Injibara, Kombolcha, and Mekaneselam bamboo-fibre-reinforced epoxy composites were 227 ± 14–171 ± 22 MPa, 255 ± 18–129 ± 15 MPa, and 206 ± 19–151 ± 11 MPa, whereas Young’s moduli were 21 ± 2.9–16 ± 4.24 GPa, 18 ± 0.8–11 ± 0.51 GPa, and 18 ± 0.85–16 ± 0.82 GPa respectively. The highest to the lowest tensile strengths and Young’s moduli of bamboo fibres and their epoxy composites were Injibara, Mekaneselam, and Kombolcha, which were the local regional area names from these fibres were extracted. The intended functional application of the current research study is the automobile industries of headliners, which substitute the conventional materials of glass fibres.