Pretend there's something in your eye.
This was my go-to from the day I got contact lenses to the day I realized it looked incredibly strange and required a lot more acting skills than I have.
Wash your hands.
Oh no, EMERGENCY. I need to run to the bathroom for the express purpose of washing my hands, and while I'm here I might as well quickly check out my hair. What did I just touch? Who knows. Something horrible probably.
Get paper towels.
Nothing to see here, just grabbing a handful of paper towels and then throwing them away.
Pretend to blow your nose.
For some reason blowing your nose in front of the person at the sink is more acceptable than checking your hair. The reason is that it's less vain.
Ask them if they've seen a phone.
More as part of a survey. Don't do this if you're holding your phone. If you're holding your phone you can ask them if they know what the date is, or if there's enough soap in the soap dispenser, or who the fifth president of the United States was, or whatever you think of first.
Wash spilled food off your shirt.
Whichever food you spilled on it most recently.
The old "count imaginary things around the room and nod."
Nod very slowly while looking upwards then leave. Are you looking for something? Are you insane? Did you just walk into the bathroom to check your hair and now that there's someone here you don't know what to do? Who knows. You seem totally normal to me.