How much preservation do you want?
If the art is VERY important to this customer, then perhaps he should find a less risky place to display it. I suggest making sure he understands the risks: mainly, paper-fiber stress and condensation from quick-changing temperature and humidity, and moisture buildup within the frame package.
If he makes an informed decision to display in the bathroom, then Rebecca's recommendation to use Hugh Phibbs' Marvelseal method method makes a lot of sense. The air space under the glazing should be generous.
Glass is gas-impermeable and inhibits transfer of everything. So, in long-term adverse conditions, glass would be better.
Acrylic is a better insulator. That is, it would take longer for condensation to form inside, so it would do a better job of slowing changes within the frame package, and inhibiting quick-change condensation.
Rebecca, please check me on this: My understanding of slica gel and other desiccants is that they work like regulators of moisture content. That is, they absorb humidity if gets is too high, and release humidity if it gets too low within the closed package. Desiccants need to be conditioned before their use; in this case, conditioned to low humidity.
However, over time, if moisture repeatedly finds its way into the frame, the desiccant could slowly re-condition itself to incresingly higher humidity.
A customer displayed framed art (not my framing) on his boat, and it got moldy. He thought the desiccant was defective, but it reconditioned itself to high moisture. Eventually, it could serve to keep humidity in the frame extraordinarily high. That would be bad, so the suggestion is to re-condition the desiccant periodically, to keep it dry.