We present the first high-significance detection (4.1σ) of the Baryon Acoustic Oscillations (BAO) feature in the galaxy bispectrum of the twelfth data release (DR12) of the Baryon Oscillation Spectroscopic Survey (BOSS) constant mass sample (0.43 ≤ z ≤ 0.7). We measured the scale dilation parameter, α, using the power spectrum, bispectrum, and both simultaneously for DR12, plus 2048 MultiDark-PATCHY mocks in the North and South Galactic Caps (NGC and SGC, respectively), and the volume-weighted averages of those two samples (N+SGC). The fitting to the mocks validated our analysis pipeline, yielding values consistent with the mock cosmology. By fitting to the power spectrum and bispectrum separately, we tested the robustness of our results, finding consistent values from the NGC, SGC, and N+SGC in all cases. We found DV = 2032 ± 24(stat.) ± 15(sys.) Mpc, DV = 2038 ± 55(stat.) ± 15(sys.) Mpc, and DV= 2031 ± 22(stat.) ± 10(sys.) Mpc from the N+SGC power spectrum, bispectrum, and simultaneous fitting, respectively. Our bispectrum measurement precision was mainly limited by the size of the covariance matrix. Based on the fits to the mocks, we showed that if a less noisy estimator of the covariance were available, from either a theoretical computation or a larger suite of mocks, the constraints from the bispectrum and simultaneous fits would improve to 1.1 per cent (1.3 per cent with systematics) and 0.7 per cent (0.9 per cent with systematics), respectively, with the latter being slightly more precise than the power spectrum only constraints from the reconstructed field.