  Observing the neutral hydrogen distribution across the Universe via
redshifted 21cm line intensity mapping constitutes a powerful probe for
cosmology. However, the redshifted 21cm signal is obscured by the foreground
emission from our Galaxy and other extragalactic foregrounds. This paper
addresses the capabilities of the BINGO survey to separate such signals.
Specifically, this paper looks in detail at the different residuals left over
by foreground components, shows that a noise-corrected spectrum is unbiased,
and shows that we understand the remaining systematic residuals by analyzing
nonzero contributions to the three-point function. We use the generalized
needlet internal linear combination, which we apply to sky simulations of the
BINGO experiment for each redshift bin of the survey. We present our recovery
of the redshifted 21cm signal from sky simulations of the BINGO experiment,
including foreground components. We test the recovery of the 21cm signal
through the angular power spectrum at different redshifts, as well as the
recovery of its non-Gaussian distribution through a bispectrum analysis. We
find that non-Gaussianities from the original foreground maps can be removed
down to, at least, the noise limit of the BINGO survey with such techniques.
Our component separation methodology allows us to subtract the foreground
contamination in the BINGO channels down to levels below the cosmological
signal and the noise, and to reconstruct the 21cm power spectrum for different
redshift bins without significant loss at multipoles $20 \lesssim \ell \lesssim
500$. Our bispectrum analysis yields strong tests of the level of the residual
foreground contamination in the recovered 21cm signal, thereby allowing us to
both optimize and validate our component separation analysis. (Abridged)
