  Cosmological information from forthcoming galaxy surveys, such as LSST and
Euclid, will soon exceed that available from the CMB. Higher order correlation
functions, like the bispectrum, will be indispensable for realising this
potential. The interpretation of this data faces many challenges because
gravitational collapse of matter is a complex non-linear process, typically
modelled by computationally expensive N-body simulations. Proposed alternatives
using fast dark matter codes (e.g. 2LPT or particle-mesh) are primarily
evaluated on their ability to reproduce clustering statistics linked to the
matter power spectrum. The accuracy of these codes can be tested in more detail
by looking at higher-order statistics, and in this paper we will present an
efficient and optimal methodology (MODAL-LSS) to reconstruct the full
bispectrum of any 3D density field. We make quantitative comparisons between a
number of fast dark matter codes and Gadget at redshift $z=0.5$. This will
serve as an important diagnostic tool for dark matter/halo mock catalogues and
lays the foundation for realistic high precision analysis with the galaxy
bispectrum. In particular, we show that the lack of small-scale power in the
bispectrum of fast codes can be ameliorated by a simple `boosting' technique
for the power spectrum. We also investigate the covariance of the MODAL-LSS
bispectrum estimator, demonstrating the plateauing of non-Gaussian errors in
contrast to simple Gaussian extrapolations. This has important consequences for
the extraction of information from the bispectrum and hence parameter
estimation. Finally we make quantitative comparisons of simulation bispectra
with theoretical models, discussing the initial parameters required to create
mock catalogues with accurate bispectra.
