In the strong-electron-phonon-coupling regime, we retrieve the stability criterion for bipolaron formation in a spherical quantum dot. The model that we use consists of a pair of electrons immersed in a reservoir of bulk LO phonons and confined within an isotropic parabolic potential box. In this particular quasi-zero-dimensional geometry, where the electrons do not have any free spatial direction to expand indefinitely, a plausible approach would be to treat the electrons either to form a bipolaronic bound state or enter a state of two close, but individual polarons inside the same dot. The confined two-polaron model adopted here involves the polaron-polaron separation introduced as an adjustable parameter to be determined variationally. It is found that the fundamental effect of imposing such a variational flexibility is to modify the phase diagram to a considerable extent and to sustain the bipolaron phase in a broader domain of stability.