The Rashba effect of surface alloys of semimetallic bismuth (Bi) is strongly related to its specific structural properties. The initial growth behaviors of Bi atoms on Ag(111) substrate and Au(111) substrate are systematically investigated by combining scanning tunneling microscopy (STM) and density flooding theory (DFT) in this paper. Continuous Ag₂Bi alloy films are formed preferentially at the step edge on Ag(111) held at room temperature; Bi atoms replace step edge atoms with low coordination number and are randomly distributed from single atoms to the forming of long-range ordered Ag₂Bi alloy phase as the coverage increases to 0.33 ML on Ag(111) held at 570 K. With the coverage increasing, Ag₂Bi is converted into Bi films with a p\times \sqrt3 structure by the dealloying process. In contrary to Ag(111), Bi growth behavior on Au(111) held at room temperature and at 570 K are consistent: Bi atoms are adsorbed preferentially on Au atom pairs with coordination 5 and are dispersed as single atoms and clusters in the densely packed region and the corners of the herringbone reconstruction when coverage level is below 0.40 ML; as the coverage level increases to 0.60 ML, the disordered Bi atoms gradually transform into the long-range ordered ( \sqrt37\times \sqrt37 ) phase. Moreover, the adsorption of Bi atoms leads the Au(111) surface strain to gradually release. The different growth behaviors of Bi atoms on Ag(111) substrate and Au(111) substrate suggest that the interaction between Bi atoms and the substrate plays a key role. Bi atoms are adsorbed preferentially around atoms with low surface coordination number under low coverage.