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, b1 and b2, 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 b1(zeff)1.40σ8(zeff) = 1.672 ± 0.060 and b20.30(zeff)σ8zeff = 0.579 ± 0.082 at the effective redshift of the survey, zeff = 0.57. The main cosmological result is the constraint on the combination f0.43(zeff)σ8(zeff) = 0.582 ± 0.084, which is complementary to f8 constraints obtained from two-point redshift-space distortion analyses. A less conservative analysis yields f0.43(zeff)σ8(zeff) = 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 f0.438 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).