For pre-employment screenings (and also believe random employer drug testing), most states, if not all, don't allow searching. They can ask you to lift up your shirt, pant leg, and empty your pockets. Stuff like that. But no frisking, patting down, etc.

If you are taking a test due to court order or other things, that's different.

As far as being supervised, I think that has to be court ordered too. Unless it's a multi-stall bathroom, in which someone would be supervising the main door (while you are in a private stall). I have never known someone to be supervised for pre-employment screenings, and all the research I've done says that it's illegal...

....unless of course you sign something that says it will be supervised and give up those rights.

I could be wrong about this. No official source, but I've had to do rounds of research on this in the past and that's what I've come up with...if you are suspicious, they can ask for a second urine sample (have seen this happen), ask questions, etc...but haven't heard of anyone being patted down or anything for being suspicious at a pre-employment screening.