Non-corroding glass fibre reinforced polymer (GFRP) bars are an attractive alternative to conventional steel reinforcement in reinforced concrete (RC) members exposed to aggressive environments. Similarly, structural health monitoring (SHM) is effective for tracking the performance of RC structures over an extended period to detect changes in behaviour or the onset of damage. Distributed strain measurement of reinforcing materials can be achieved using distributed fibre optic sensors (DFOS). DFOS offer high sensitivity, precision, small size, resistance to corrosion, high resolution, and long-term measurement stability. Developing reinforcing bars with strain-sensing capabilities, achieved by attaching DFOS cables along their length, has been proposed as a novel solution for accurate real-time measurements of the bar’s strain distribution and crack monitoring of RC members. Pultruded GFRP reinforcing bars, known for their high durability and unidirectional properties, possess attributes favourable for packaging with DFOS, forming a multifunctional composite material system. The findings of a feasibility study are presented in this paper in which GFRP bars instrumented with surface-bonded DFOS were tested under uniaxial tension. Investigated parameters include the type of loading (monotonic, sustained, and cyclic) and DFOS attachment technique (surface-mounted versus embedded within longitudinal groove, both using two-part epoxy). The experimental results show that the DFOS were able to reliably measure the GFRP bar strains within the serviceability loading ranges, while permanent loss of distributed monitoring efficiency was observed under high sustained strain conditions.