We analyze the polarization dependence of photoelectron momentum maps observed in one-photon photoemission (1PPE) and two-photon photoemission (2PPE) from clean Cu(111) surfaces and from surface alloys of Bi on Cu(111). For clean Cu(111), we find similar emission patterns and a similar polarization dependence in 1PPE and 2PPE due to the dominating influence of direct optical transitions between initial and final bulk states. In contrast, on the Bi/Cu(111) surface, we observe significantly different emission patterns between linear and nonlinear photoemission measurements. This behavior is assigned to the presence of unoccupied states, which favor surface two-photon transitions specific to the Bi surface alloy and suppress the strong bulk contribution seen in 1PPE. The polarization dependence of the 2PPE momentum patterns can be assigned to the properties of the occupied states of the Bi/Cu(111) surface alloy, which we analyze with the help of one-step photoemission calculations.