is there a heated clothes dryer that would plug into bathroom socket

[eastdulwichbedwetter]

Like the lakeland one www.lakeland.co.uk/p21736/Lakeland-Dry-Soon-Range

that would plug into a bathroom two pin plug?

No.

If you in the UK, you will be thinking of a shaver socket. It is very low power.

I used to use my epilator with a 3 pin plug plugged into shaver socket using one of the international travel adapters, may have been the European one. However, I'm not sure how safe it is or whether the heater would get hot enough.