We analyse the anisotropic clustering of the Baryon Oscillation Spectroscopic Survey CMASS Data Release 11 sample, which consists of 690 827 galaxies in the redshift range 0.43 < z < 0.70 and has a sky coverage of 8498 deg2 corresponding to an effective volume of ∼ 6 Gpc3. We fit the Fourier space statistics, the power spectrum and bispectrum monopoles to measure the linear and quadratic bias parameters, b 1 and b 2, for a non-linear non-local bias model, the growth of structure parameter f and the amplitude of dark matter density fluctuations parametrized by σ8. We obtain b 1(z eff)1.40σ8(z eff) = 1.672 ± 0.060 and $b_2^{0.30}(z_{\rm eff})\sigma _8(z_{\rm eff})=0.579\pm 0.082$ at the effective redshift of the survey, z eff = 0.57. The main cosmological result is the constraint on the combination f 0.43(z eff)σ8(z eff) = 0.582 ± 0.084, which is complementary to fσ8 constraints obtained from two-point redshift-space distortion analyses. A less conservative analysis yields f 0.43(z eff)σ8(z eff) = 0.584 ± 0.051. We ensure that our result is robust by performing detailed systematic tests using a large suite of survey galaxy mock catalogues and N-body simulations. The constraints on f 0.43σ8 are useful for setting additional constraints on neutrino mass, gravity, curvature as well as the number of neutrino species from galaxy surveys analyses (as presented in a companion paper).