We measure and analyse the bispectrum of the final, Data Release 12, galaxy
sample provided by the Baryon Oscillation Spectroscopic Survey, splitting by
selection algorithm into LOWZ and CMASS galaxies. The LOWZ sample contains
361762 galaxies with an effective redshift of $z_{\rm LOWZ}=0.32$, and the
CMASS sample 777202 galaxies with an effective redshift of $z_{\rm
CMASS}=0.57$. Combining the power spectrum, measured relative to the
line-of-sight, with the spherically averaged bispectrum, we are able to
constrain the product of the growth of structure parameter, $f$, and the
amplitude of dark matter density fluctuations, $\sigma_8$, along with the
geometric Alcock-Paczynski parameters, the product of the Hubble constant and
the comoving sound horizon at the baryon drag epoch, $H(z)r_s(z_d)$, and the
angular distance parameter divided by the sound horizon, $D_A(z)/r_s(z_d)$. We
find $f(z_{\rm LOWZ})\sigma_8(z_{\rm LOWZ})=0.460\pm 0.066$, $D_A(z_{\rm
LOWZ})/r_s(z_d)=6.74 \pm 0.22$, $H(z_{\rm LOWZ})r_s(z_d)=(11.75\pm
0.55)10^3\,{\rm kms}^{-1}$ for the LOWZ sample, and $f(z_{\rm
CMASS})\sigma_8(z_{\rm CMASS})=0.417\pm 0.027$, $D_A(z_{\rm
CMASS})/r_s(z_d)=9.33 \pm 0.15$, $H(z_{\rm CMASS})r_s(z_d)=(13.78\pm
0.28)10^3\,{\rm kms}^{-1}$ for the CMASS sample. We find general agreement with
previous BOSS DR11 and DR12 measurements. Combining our dataset with Planck we
perform a null test of General Relativity (GR) through the
$\gamma$-parametrisation finding $\gamma=0.719^{+0.080}_{-0.072}$, which
reveals a $\sim2.5\sigma$ tension with the GR predictions. We ensure that our
measurements are robust by performing detailed systematic tests using a suite
of survey galaxy mock catalogs and $N$-body simulations.