For laboratory demonstrations, Lamb wave detection using fiber Bragg grating (FBG) sensors is typically performed with only the grating location spot bonded and with the fiber axis aligned with the ultrasonic propagation direction. However, in reality, the entire length of fiber is often bonded to protect the fiber from any environmental damage, referred to here as continuous bonding. Theoretically, the Lamb wave signal can couple to the guided traveling wave in the optical fiber at any adhered location, which could potentially produce output signal distortion. In this paper, we investigate the impact of continuously bonding a long length of optical fiber on the measured Lamb wave signal detected by an FBG. Therefore, an experiment is performed to measure the Lamb wave signals excited from a PZT actuator using a surface bonded FBG with varying optical fiber bond length, indicating that the output FBG response remains constant with changing length. The second experiment investigates the FBG angular response to the traveling wave in the optical fiber, and compares to the conventional case where FBG directly measures the Lamb waves with varying angle. Specifically, the optical fiber is bonded to the plate at a distance away from the FBG. The Lamb wave is launched to the bond location with varying angles, which is coupled to traveling wave, then measured with FBG. The results indicate that the mechanism of the Lamb wave transfer to the directly bonded FBG is through displacement matching, whereas that of the traveling wave is through a forced excitation.