The peroxide used in bleaching causes an oxidative process, and we know that oxidation can be harmful to tissues and cells. But we don't know whether that can affect either you or your baby. There's another whitening process called microabrasion that uses acidic components to remove stains, but we have even less data on the safety of that in pregnancy.
So just to be on the safe side, I strongly recommend that women wait until the pregnancy is over and they're done nursing to have their teeth bleached — or to use any over-the-counter tooth bleaching products.
In fact, I always advise patients to seek a dentist's advice before using any over-the-counter whitening products. Tooth discoloration can be a sign of a bigger problem (such as the death of the pulp tissue in the tooth), and a correct diagnosis can only be made by a dentist.