We present a phenomenological modification of the standard perturbation theory prediction for the bispectrum in redshift space that allows us to extend the model to mildly non-linear scales over a wide range of redshifts, z ≤ 1.5. Our model require 18 free parameters that are fitted to N-body simulations using the shapes k2/k1 = 1, 1.5, 2.0, 2.5. We find that we can describe the bispectrum of dark matter particles with ∼ 5% accuracy for ki ≲ 0.10h/Mpc at z = 0, for ki ≲ 0.15h/Mpc at z = 0.5, for ki ≲ 0.17h/Mpc at z = 1.0 and for ki ≲ 0.20h/Mpc at z = 1.5. For very squeezed triangles with k1 = k2 ≳ 0.1 hMpc-1 and k3 ≤ 0.02 hMpc-1, however, neither SPT nor the proposed fitting formula are able to describe the measured dark matter bispectrum with this accuracy. We show that the fitting formula is sufficiently general that can be applied to other intermediate shapes such as k2/k1 = 1.25, 1.75, and 2.25. We also test that the fitting formula is able to describe with similar accuracy the bispectrum of cosmologies with different Ωm, in the range 0.2 ≲ Ωm ≲ 0.4, and consequently with different values of the logarithmic grow rate f at z = 0, 0.4 ≲ f(z = 0) ≲ 0.6. We apply this new formula to recover the bias parameters, f and σ8, by combining the redshift space power spectrum monopole and quadrupole with the bispectrum monopole for both dark matter particles and haloes. We find that the combination of these three statistics can break the degeneracy between b1, f and σs. For dark matter particles the new model can be used to recover f and σs with ∼ 1% accuracy. For dark matter haloes we find that f and σs present larger systematic shifts, ∼ 10%. The systematic offsets arise because of limitations in the modelling of the interplay between bias and redshift space distortions, and represent a limitation as the statistical errors of forthcoming surveys reach this level. Conveniently, we find that these residual systematics are mitigated for combinations of parameters. In particular, the quantity fσs is still recovered with ∼ 1% accuracy for the particular halo population and cosmology studied. The improvement on the modelling of the bispectrum presented in this paper will be useful for extracting information from current and future galaxy surveys.