We investigated Fe-substitution effects on ferromagnetic fluctuations in the superconducting overdoped and nonsuperconducting heavily overdoped regimes of the Bi-2201 cuprates by the magnetization and electrical-resistivity measurements. It was found that the spin-glass state was induced at low temperatures by the Fe substitution. The Curie constant and the effective Bohr magneton, estimated from the magnetic susceptibility, as well as the dimensionality of the ferromagnetic fluctuations from the resistivity, suggest the enhancement of the ferromagnetic fluctuations owing to the Fe subsutitution. A ferromagnetic spin-cluster model is proposed in the heavily overdoped regime of Bi-2201, while an antiferromagnetic spin-cluster model has been proposed in the overdoped regime of Bi-2201 [Hiraka et al., Phys. Rev. B 81, 144501 (2010].