The fluid-filled amniotic sac begins to protrude from the vulva as the pup begins making its way through the birth canal. It may take several pushes before the pup and its placenta are fully delivered. Sometimes a placenta is retained, but it's usually pushed out before the next pup's arrival.
This brings up the issue of when you'll see the mother's water break. Sometimes the sac will rupture as it emerges from the vulva. You can expect delivery within minutes or even seconds of this happening. Other times, the puppy is still in the sac after delivery, and the mother will chew the sac to open it. This releases the fluid, and then the mother will clean the pup's face and stimulate it to begin breathing. If you see the bitch is bleeding a little at this point, it's natural.
Dogs don't bleed before labor unless there is some kind of complication, such as premature separation of a sac from the uterus, but it's not unusual for the mother to get a small tear in her vulva when pushing out the first pup. Most tears heal quickly on their own after the litter is delivered.