We investigated the behavior of edge states in two-dimensional bilayered Bi nanoribbons by atom adsorption based on the density functional method. We found that for a clean Bi zigzag ribbon the penetration depth of well-localized edge states is a function of the momentum-space width of the edge-state dispersion. Depending on the density of adsorbed H, Br and I atoms, respectively, the edge state can be changed from localized within a very narrow region to delocalized over the whole region in real space. Changes in atomic and electronic structures and topological insulator properties associated with the atomic adsorption on the edges of zigzag bilayer nanoribbon (ZBNR) are discussed. Our work suggests that ZBNR could be a possible candidate for nanoelectronic devices under some special conditions.