  Primordial black holes represent a unique probe to constrain the early
universe on small scales - providing the only constraints on the primordial
power spectrum on the majority of scales. However, these constraints are
strongly dependent on even small amounts of non-Gaussianity, which is
unconstrained on scales significantly smaller than those visible in the CMB.
This paper goes beyond previous considerations to consider the effects of a
bispectrum of the equilateral, orthogonal and local shapes with arbitrary
magnitude upon the abundance of primordial black holes. Non-Gaussian density
maps of the early universe are generated from a given bispectrum and used to
place constraints on the small scale power spectrum. When small, we show that
the skewness provides an accurate estimate for how the constraint depends on
non-Gaussianity, independently of the shape of the bispectrum. We show that the
orthogonal template of non-Gaussianity has an order of magnitude weaker effect
on the constraints than the local and equilateral templates.
