In this article, we consider the bilinear operator T satisfying that there exists a positive constant C(T), depending on T, such that, for any measurable functions f and g with compact support, tââ with 0<|t|â€1, and xâân with 0âsupp(f(xâtâ
))â©supp(g(xââ
)), T(f,g)(x)â€C(T)â«ânf(xâty)g(xây)|y|ndy. We investigate the boundedness of T on the vanishing generalized Morrey spaces V0Lp,Ï(ân) and VâLp,Ï(ân), and the boundedness of the subbilinear maximal operator âł on the vanishing generalized Morrey space V(â)Lp,Ï(ân), and their applications to some classical (sub)bilinear operators in harmonic analysis. As a byproduct, we also show that T is bounded on generalized Morrey spaces Lp,Ï(ân). Some typical examples for the main results of this paper are also included.