I want to put a sensor in my bathroom to catch anyone who comes in through the window. Do I need to buy a particular type of sensor which will be immune to the damper atmosphere found in a bathroom?

Don't would the best idea

you can but you should use an external rated sensor. There are sealed units available. Or you can look at protecting the window if thats the risk.

I want to protest this room because the window gets left open during the heat of summer. So i'm not sure how I could protect the window with a switch. Are there any externally rated sensors that look like an ordinary internal sensor?

The window being open is more of an issue. Do you want to leave the window open but still arm the alarm?

More to the point most properties rely on a PIR on the landing to provide protection for what your after, don't think I've ever seen a PIR in a bathroom/loo, contact on window in a few instances.

Having the window open would possible cause false alarms anyways . You would be better off with a contact on the door or pir on the landing . Or fit a restraining bar on the window so it cannot be opened too far an fit a contact on the hinge side . So if it's opened past a certain point it wild activate .

Hope that helps

Got shock sensors out there for years with no issues in bathrooms. As long as not facing a busy road I can see no issue and set correctly it can detect someone crawling through.

(Obviously cable intake is from the bottom!! Or rear if able to chase a cable and feed through).

Also if leaving open as suggested a steel bar either across or vertically mounted would assisst.

I would put a detector on the landing or hallway outside the bathroom, nobodys gonna steal your toothbrush they will come out of the bathroom the alarm will go off and they will leggit

the alarm will go off and they will leggit

hopefully