Discuss this with your birth attendants. Many people feel comfortable with the time that it takes for the mother to reach down and pick up her baby. Any longer than that is not necessary. The baby begins to breathe when its face breaks the surface of the water and comes into contact with the air. Until then, the baby receives oxygen through its umbilical cord.
Some people choose to stay in the tub after the birth and bond with the baby.
Because of this, they also choose to birth their placentas in the tub. This is something that should be discussed with your birth attendant. Dr. Michael Rosenthal reports that there have been no incidences of infection in close to the 1000 births that he has attended. This may be due to the fact that in labor, everything is moving down and out. With the baby coming down the birth canal, it does not make sense that bacteria could move up into the uterus.