There is a possibility for a dog to bleed after she has been spayed, but it should be brought to the attention of a vet because it can indicate a problem post-op. However, a dog will not go into heat without a uterus and should not experience menstrual bleeding as she traditionally would prior to being spayed.
The main reason to spay a dog is to prevent pregnancy. The benefits of spaying include a decreased risk of uterine tumors, breast cancer and behavior problems. In general, female dogs should be spayed before the first heat, which is generally between the ages of 5 and 7 months. Spaying while the dog is in heat may pose additional risks.