A standard fly mask is not generally used while riding, as the stiff mesh interferes with the bridle and the minimal visual impairment of the mesh still presents a safety issue. Other styles of insect protection gear are designed for use with a bridle.
One design is a crochet-like "bonnet" for the ears only, designed to be worn under a bridle without rubbing. The other is a soft, very fine mesh face and nose-covering mask designed to be worn with a bridle and not impair vision, but not sturdy enough to withstand turnout.