The large bipolaron in two and three dimensions is investigated by combining anapproximate wave functions for the relative motion and the modified Lee-Low-Pines variational method. The values of the critical coupling constant αc above which bipolarons may exist and the critical ratio of dielectric constants ηc below which bipolarons may exist are evaluated, which are very close to the recent results obtained within a totally different variational approach. In addition, the stability region of bipolarons in the 1/α,η plane is clearly plotted. It is also found that low dimensional materials are more favorable for the formation of bipolarons.