  The bispectrum is a 3-point statistic with the potential to provide
additional information beyond power spectra analyses of survey datasets. Radio
telescopes which broadly survey the 21cm emission from neutral hydrogen (HI)
are a promising way to probe LSS and in this work we present an investigation
into the HI intensity mapping (IM) bispectrum using simulations. We present a
model of the redshift space HI IM bispectrum including observational effects
from the radio telescope beam and 21cm foreground contamination. We validate
our modelling prescriptions with measurements from robust IM simulations,
inclusive of these observational effects. Our foreground simulations include
polarisation leakage, on which we use a Principal Component Analysis cleaning
method. We also investigate the effects from a non-Gaussian beam including
side-lobes. For a MeerKAT-like single-dish IM survey at $z=0.39$, we find that
foreground removal causes a 8% reduction in the equilateral bispectrum's
signal-to-noise ratio $S/N$, whereas the beam reduces it by 62%. We find our
models perform well, generally providing $\chi^2_\text{dof}\sim 1$, indicating
a good fit to the data. Whilst our focus is on post-reionisation, single-dish
IM, our modelling of observational effects, especially foreground removal, can
also be relevant to interferometers and reionisation studies.
