We have performed inelastic neutron scattering measurements on the single-layer cuprate Bi(2+x) Sr(2-x) CuO(6+y) (Bi2201) with x = 0.2, 0.3, 0.4, and 0.5, a doping range that spans the spin-glass to superconducting phase boundary. The doping evolution of low energy spin fluctuations (11 </~ meV) was found to be characterized by a change in the incommensurate modulation wave vector from the tetragonal [110] to [100]/[010] directions, while maintaining a linear relation between the incommensurability and the hole concentration, δ ≈ p. In the superconducting regime, the spectral weight is strongly suppressed below ≈ 4 meV. Similarities and differences in the spin correlations between Bi2201 and the prototypical single-layer system La(2-x) Sr(x)CuO(4) are discussed.