Does a new violin bow come complete with bow string?”
That stringy stuff on the bow is horsehair, or on the cheapest bows, nylon. The hair comes from the tails of horses or ponies. A new bow comes haired. After playing for a while (a few months or years depending on how often and how violently you play) the bow must be rehaired. This requires a skilled craftsman and usually costs $50 to $75 depending on what part of the country you live in. Cheap fiberglas kiddie bows can usually be bought for less than the cost of a professional rehair. A decent student grade Pernambuco or Brazilwood bow will cost enough to warrant rehairing. At any rate, they all start out with a full head of hair.