Any time you don't have similar moisture absorbtion (i.e., different finishes) on both sides of a wood panel, the panel can warp. A bathroom can have some significant humidity levels if it contains a shower or even a bath. I'd be leary. Are you going to cover the stain with a topical finish like urethane? If so, then having one side stained and the other shouldn't make much difference. If it is going to be natural...you may.