The nonlinear evolution of magnetic islands is investigated in regimes with a high fraction of bootstrap current density, which are of great interest for advanced tokamak scenarios. For a sufficiently large fraction of the equilibrium bootstrap current density (measured against the local magnetic shear and the poloidal magnetic fields), the nonlinear island growth and the saturated magnetic island width are found to depend neither on the original local equilibrium magnetic shear nor on the fraction of the bootstrap current density. In addition, in the positive magnetic shear region the magnetic islands together with its rational surface move inwards. The results of corresponding numerical simulations agree well with analytical predictions.