I have been a Suzuki Violin teacher for over five years. I have always recommended that very young students use the fiberglass bows that are available. The parents of one of my younger students purchased a violin kit with a wood bow. It does make a difference. The popularity of fiberglass bows arises from the fact that fiberglass is more sturdy than bows made of wood.
Wooden bows are more vulnerable to damage from mistreatment.
This becomes an more important factor when students are not properly trained to handle and care for the bow. Even the youngest students can, and should, get proper training so that they can use wood bows. Fiberglass bows may be robust and otherwise adequate for beginning students, but the lighter weight and thinner shaft of the wood bow is superior for study. Parents should only purchase or rent bows, and violins for that matter, that are returnable, subject to the teacher's approval. You should make certain that the bow is straight and not warped.