While Gandalf is often depicted riding Shadowfax without a bridle in illustrations and adaptations, the books never explicitly state that he does. In fact, it's implied that he does use a bridle:
* In the books, Gandalf always speaks of "reining in" Shadowfax, which implies the use of a bridle.
* There are descriptions of Gandalf's riding gear, including a "silver-studded bridle" in The Fellowship of the Ring.
* The movies depict Gandalf with a bridle, likely for practical reasons to control the horse.
It's possible the image of Gandalf riding without a bridle originated from the iconic illustration by Alan Lee, which shows Shadowfax without a bridle. However, this artistic choice is not supported by the text.
So, while the image is powerful and often memorable, it's not accurate to say that Gandalf rode without a bridle in the books.