  It has been shown that a three-point correlation function of tensor
perturbations from a bounce model in general relativity with a
minimally-coupled scalar field is highly suppressed, and the resultant
three-point function of cosmic microwave background (CMB) B-mode polarizations
is too small to be detected by CMB experiments. On the other hand, bounce
models in a more general class with a non-minimal derivative coupling between a
scalar field and gravity can predict the three-point correlation function of
the tensor perturbations without any suppression, the amplitude of which is
allowed to be much larger than that in general relativity. In this paper, we
evaluate the three-point function of the B-mode polarizations from the general
bounce cosmology with the non-minimal coupling and show that a signal-to-noise
ratio of the B-mode auto-bispectrum in the general class can reach unity for
$\ell_{\rm max}\geq9$ and increase up to $5.39$ for $\ell_{\rm max}=100$ in the
full-sky case. We also discuss the possibility to test the general class of
bounce models by upcoming CMB experiments.
