My grandfather used to get the power for his amateur radio equipment in his shed via one of these in the bathroom.
You would be better off with something earthed though so run an extension lead fitted with an RCD plug into the bathroom when you need it. It's not really any more dangerous than having electricity in the kitchen. I'm sure there is a way of having a permanent 13A socket in a bathroom under current regulations but I don't recall what it was. I think someone told me about it a few years ago (or I dreamed it!).
Another option would be a shaver socket designed for a bathroom if there is one available of suitable wattage as these have an isolating transformer.
Just do what is done in industry. Do a risk assessment. Think of all of the things which could happen which could result in electrocution (and I bet you can't find many) then think of the likelihood of any of them occurring. Anything you find unsafe which is likely to happen needs to be addressed.
Don't include ridiculous things (like some people at work do) such as using the enlarger whilst taking a bath and wearing a tin foil hat in a thunderstorm.
EDIT: All of the shaver sockets I have found are only rated at 20 watts which isn't enough. Another option if you have an enlarger with a twelve volt bulb and separate power supply is to put the power supply in another room and just run the twelve volt supply into the bathroom with a suitably thick cable.