  We constrain the linear and quadratic bias parameters from the configuration
dependence of the three-point correlation function (3PCF) in both redshift and
projected space, utilizing measurements of spectroscopic galaxies in the Sloan
Digital Sky Survey (SDSS) Main Galaxy Sample. We show that bright galaxies (M_r
< -21.5) are biased tracers of mass, measured at a significance of 4.5 sigma in
redshift space and 2.5 sigma in projected space by using a thorough error
analysis in the quasi-linear regime (9-27 Mpc/h). Measurements on a fainter
galaxy sample are consistent with an unbiased model. We demonstrate that a
linear bias model appears sufficient to explain the galaxy-mass bias of our
samples, although a model using both linear and quadratic terms results in a
better fit. In contrast, the bias values obtained from the linear model appear
in better agreement with the data by inspection of the relative bias, and yield
implied values of sigma_8 that are more consistent with current constraints. We
investigate the covariance of the 3PCF, which itself is a measurement of galaxy
clustering. We assess the accuracy of our error estimates by comparing results
from mock galaxy catalogs to jackknife re-sampling methods. We identify
significant differences in the structure of the covariance. However, the impact
of these discrepancies appears to be mitigated by an eigenmode analysis that
can account for the noisy, unresolved modes. Our results demonstrate that using
this technique is sufficient to remove potential systematics even when using
less-than-ideal methods to estimate errors.
