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Context. The 21 cm hydrogen line is arguably one of the most powerful probes with which to explore the Universe, from recombination to the present times. To recover it, it is essential to separate the cosmological signal from the much stronger foreground contributions at radio frequencies. The Baryon Acoustic Oscillations from Integrated Neutral Gas Observations (BINGO) radio telescope is designed to measure the 21 cm line and detect baryon acoustic oscillations (BAOs) using the intensity mapping (IM) technique. Aims. This work analyses the performance of the Generalized Needlet Internal Linear Combination (GNILC) method when combined with a power spectrum debiasing procedure. This method was applied to a simulated BINGO mission, building upon previous work from the collaboration. It compares two different synchrotron emission models and different instrumental configurations and takes into account ancillary data in order to optimize both the removal of foreground emission and the recovery of the 21 cm signal across the full BINGO frequency band and to determine an optimal number of frequency (redshift) bands for the signal recovery. Methods. We produced foreground emission maps using the Planck Sky Model (PSM) and generated cosmological HI emission maps using the Full-Sky Log-normal Astro-Fields simulation Kit (FLASK) package. We also created thermal noise maps according to the instrumental setup. We apply the GNILC method to the simulated sky maps to separate the HI plus thermal noise contribution and, through a debiasing procedure, recover an estimate of the noiseless 21 cm power spectrum. Results. We find a near-optimal reconstruction of the HI signal using an 80-bin configuration, which resulted in a power-spectrum reconstruction average error over all frequencies of 3%. Furthermore, our tests show that GNILC is robust against different synchrotron emission models. Finally, adding an extra channel with C-Band All-Sky Survey (CBASS) foregrounds information, we reduced the estimation error of the 21 cm signal. Conclusions. The optimization of our previous work, producing a configuration with an optimal number of channels for binning the data, significantly impacts decisions regarding BINGO hardware configuration before commissioning. We were able to recover the HI signal with good efficiency in the harmonic space, but have yet to investigate the effect of 1/f noise in the data, which will possibly impact the recovery of the HI signal. This issue will be addressed in forthcoming work. [ABSTRACT FROM AUTHOR]