Fit the socket out side the bathroom rcd protected definately, you have some profit.Inform your customer that they must not use any portable electrical appliance in the bathroom. Stick to the law strictly to protect yourself. I pray most of these answers do not come from qualified electricians(except humorous ones).
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Surely if the socket is only installed outside the bathroom as a result of the customer wanting to use the dryer in the bathroom, then it amounts to the same set of risks - she's blatantly going to use the dryer in the bathroom.
I think some of the answers you disagree with were exploring the safety and purpose of regs in a broader sense, rather than just making sure the OP gets profit and keeps out of trouble personally.
In my opinion a handheld hairdryer should not be used in a wet area. It might not be the OP's problem if she does... But overall it's better to educate and look after a customer's interests than it is simply to protect yourself against a claim. The perfect solution exists, it's a wall fixed hairdryer. They're designed for exactly this situation.