Are you using the GFI plug in the bathroom. A hair dryer in good condition shouldn't blow a 15 amp breaker. A 1500 watt hair dryer should still pull under 15 amps. I would try it in an outlet on a different circuit and see if it works. I would say either a bad dryer, outlet, or circuit breaker.
Roger & Cheryl Full Time since 2002, RVing since 1975 2008 Chevy 3500 Crew Cab Dually, 2012 RW 36RL