This study presents the development of a novel unfolding program based on a Bayesian method for Bonner spheres spectrometry. The program incorporates a priori information on the neutron spectrum, employing a linear superposition of three non-negative parametric functions: thermal-Maxwellian distribution, an intermediate region represented by a straight line in lethargy space (1/E behavior), and the Watt fission distribution for the fast region. The effectiveness of the developed program was validated through its application to two reference cases from the EURADOS 2018 exercise (LINAC and Skyshine), followed by its implementation in characterizing the neutron field around an OB26 neutron irradiator at the Secondary Standards Dosimetry Laboratory (SSDL) of the Nuclear Research Center of Algiers (CRNA), Algeria. While validation results for the LINAC case were promising, achieving comparable neutron spectrum shape and integral quantities to the reference, challenges were encountered with the Skyshine case. However, these challenges were partially addressed through sensitivity analysis, resulting in slightly improved outcomes compared to the previous participation and to the reference. Application of the program to characterize the neutron field around the OB26 irradiator yielded satisfactory results when compared to reference data. A two-step sensitivity analysis further enhanced the outcomes, initially substituting the Watt fission distribution with the evaporation distribution, thereby improving spectrum shape and integral quantities. Subsequently, utilizing the obtained neutron spectra as prior information for unfolding codes MAXED and GRAVEL ensured stability and agreement with reference data and preliminary results.