  We derive a quasiclassical expression for the density of states (DOS) of an
arbitrary, ultracold, $N$-atom collision complex, for a general potential
energy surface (PES). We establish the accuracy of our quasiclassical method by
comparing to exact quantum results for the K$_2$-Rb and NaK-NaK systems, with
isotropic model PESs. Next, we calculate the DOS for an accurate NaK-NaK PES to
be 0.124~$\mu$K$^{-1}$, with an associated Rice-Ramsperger-Kassel-Marcus (RRKM)
sticking time of 6.0~$\mu$s. We extrapolate the DOS and sticking times to all
other polar bialkali-bialkali collision complexes by scaling with atomic
masses, equilibrium bond lengths, dissociation energies, and dispersion
coefficients. The sticking times calculated here are two to three orders of
magnitude shorter than those reported by Mayle et al. [Phys. Rev. A 85, 062712
(2012)]. We estimate dispersion coefficients and collision rates between
molecules and complexes. We find that the sticking-amplified three-body loss
mechanism is not likely the cause of the losses observed in the experiments.
