Quasi-distributed smart sensing systems using fiber Bragg grating arrays have found many practical applications in structure health, electricity grid, aerospace, etc. However, the broadband light sources used for the sensing system are generally constrained to the telecom C-band, limiting the available number of sensors, hence hindering deployment of massive sensing heads for the next generation of Internet of Things (IoT) and integrated sensing and communication. Here, we demonstrate a hybrid sensing system enabled by an ultra-broadband Bi/Er co-doped fiber (BEDF) light source pumped at 830 nm. Leveraging the global excitation capability of the λ=830 nm pump, the source provides an unprecedented operating bandwidth spanning from O- to L-bands. Quasi-distributed sensing of the temperature and strain for 21 spatially separated nodes is demonstrated using the single BEDF-based Mach-Zehnder interferometer and 20 fiber Bragg gratings. Our proof of the principle system exhibits the maximum temperature sensitivity of 56 pm/℃ and maximum strain sensitivity of 0.9 pm/με. To address the issue of the colored noise measured across the spectrum arising from the source itself due to different contributions of varying environmentally sensitive defects responsible for Bi emission, not present in the Er component, we propose the use of data-driven statistical learning methods to quantitatively characterize and mitigate the measurement uncertainties that limit their applicability in precision sensing. Specifically, an adaptive residual bootstrap strategy for uncertainty quantification is used here for the first time, providing a more accurate evaluation of system uncertainty than the conventional normal distribution analysis. The system achieves measurement uncertainties of less than 4.1% for the temperature and 6.4% for the strain. Overall, the proposed sensing system has the huge potential for practical applications in large-scale structural health monitoring, the IoT, etc.