  Relativistic and free-streaming particles like neutrinos leave imprints in
large scale structures (LSS), providing probes of the effective number of
neutrino species $N_{\rm eff}$. In this paper, we use the Fisher formalism to
forecast $N_{\rm eff}$ constraints from the bispectrum (B) of LSS for current
and future galaxy redshift surveys, specifically using information from the
baryon acoustic oscillations (BAOs). Modeling the galaxy bispectrum at the
tree-level, we find that adding the bispectrum constraints to current CMB
constraints from Planck can improve upon the Planck-only constraints on $N_{\rm
eff}$ by about 10\% -- 40\% depending on the survey. Compared to the Planck +
power spectrum (P) constraints previously explored in the literature, using
Planck+P+B provides a further improvement of about 5\% -- 30\%. Besides using
BAO wiggles alone, we also explore using the total information which includes
both the wiggles and the broadband information (which is subject to systematics
challenges), generally yielding better results. Finally, we exploit the
interference feature of the BAOs in the bispectrum to select a subset of
triangles with the most information on $N_{\rm eff}$. This allows for the
reduction of computational cost while keeping most of the information, as well
as for circumventing some of the shortcomings of applying directly to the
bispectrum the current wiggle extraction algorithm valid for the power
spectrum. In sum, our study validates that the current Planck constraint on
$N_{\rm eff}$ can be significantly improved with the aid of galaxy surveys
before the next-generation CMB experiments like CMB-Stage 4.
