We have performed inelastic neutron scattering measurements on the single-layer cuprate Bi2+xSr2−xCuO6+y (Bi2201) with x=0.2, 0.3, 0.4 and 0.5, a doping range that spans the spinglass (SG) to superconducting (SC) phase boundary. The doping evolution of low energy spin fluctuations ( 11 meV) was found to be characterized by a change of 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 SC 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 La2−xSrxCuO4 are discussed.The relevance of charge and spin stripes to the phenomenology of hole-doped cuprate superconductors has been gaining currency in recent years. For example, intriguing similarities in the transport properties of stripeordered cuprates and YBa 2 Cu 3 O 6+y (YBCO) in a high magnetic field have been demonstrated [1,2]. In fact, direct evidence for field-induced charge-stripe order in YBCO was recently obtained in a nuclear magnetic resonance study [3]. The impact of stripe order on the Fermi surface [4,5] has been proposed as one possible explanation for the appearance of quantum oscillations [6,7] (though there are challenges with the simplest approaches [8]). There is also evidence of closely related nematic order [9] from Nernst-effect measurements on YBCO [10] as well as from spectroscopic imaging of Bi 2 Sr 2 CaCu 2 O 8+y with scanning tunneling microscopy (STM) [11,12].Some of the most stimulating evidence comes from real-space imaging of electronic modulations by STM in Bi 2 Sr 2 CaCu 2 O 8+y [13][14][15] and in Bi 2−x Pb x Sr 2−z La z CuO 6+y [16].These short-range correlations are found to have a period of approximately 4a, where a = 3.8Å is the lattice spacing along a Cu-O bond direction. The corresponding wave vector of the modulations, q STM , is ( 1 4 , 0, 0) in reciprocal lattice units (2π/a); q STM is observed to decrease with doping, varying in the range of 0.3 to 0.15 [15,16].Identifying q STM with the wave vector q co associated with charge stripe order in cuprates such as La 2−x Ba x CuO 4 [17] leads to a conundrum, as q co grows with doping (at least for hole concentrations p 1/8 [18]), opposite to the behavior of q STM . When spin stripe order also occurs, antiferromagnetic spin correlations are modulated at q so = 1 2 q co . It is often possible to observe incommensurate (IC) spin fluctuations split about the antiferromagnetic wave vector Q AF by q δ ≈ q so even when there is no significant stripe order, as in La 2−x Sr x CuO 4 (LSCO) [19,20]. Among possible resolutions of the conundrum, it might be that the nature of stripe correlations is not universal among different cuprate families, or that q STM measures something complementary to q co .In this Letter, we present the results of inelastic neutron scattering measurements of low-energy spin excitations in the sys...