is it possible to make a bathroom humid enough to conduct electricity?

With high enough voltage everything becomes conductive.

ELI5?
- This here is the Volt family.
  
  Marty volt is small and so he can jump across a small stream. Put up a small net and it’s impossible for him
  
  Victor, though. He’s got some strong legs. He can jump the net and the stream.
  
  In fact, he’s so strong he can jump over a small river but not if you put a small wall across the way. Then, even with a running jump, he’ll be blocked.
  
  And finally there’s Kal, ahem, Clark Volt. He’s super strong. So strong it could be an ocean and with a little jaunt before leaping he’d jump it.
  
  The stronger the volt, the further they can go and the bigger the obstacle you need to make it impossible for them to make it.
  
  So high enough voltage can literally leap through air (that’s the arcing you see in power plants shorting or lightning) or even wood itself. Even rubber, with a high enough voltage, will be conductive since the sheer force of the current will find a path for the charge.
  
  That’s also why we have lighting rods, it’s easier to redirect the current to a safe spot made to handle it than to try and make high skyscrapers out of a material that can resist the insane charges of lightning and still be strong enough and light enough to build with.
- Lightning is just air conducting electricity. Air is not typically considered a conductor.
- Everything can have a positive or negative charge. Voltage is just the difference in charge between two points. Given a big enough difference in charge any material can conduct electricity to balance the charge since nature seeks to balance out differences in charge/energy.
- You can think of voltage as the force that pushes electrons through a substance. Different substances have different amounts of resistance which blocks the electrons. However with enough voltage you can overcome that resistance and push on through. Lightning for example has a very high voltage, as it travels through air which is not very conductive.
He'll, skipped that and hold the wire between two hands (don't do that, it cannot be stressed enough how much of a bad idea that is. You wanna commit die? That is by far the most efficient way of doing it, so DONT)

ElectroBOOM has a good video related to your question. He's demonstrating with a bucket of water rather than humid air but it shows what's needed to complete the circuit.

Please do not try this at home.

that makes sense, that video was very educational, I didn't realize that it wasn't the water itself that was conductive but the contents in the water. Knowing that, it does make a bit more sense.
- Yeah I remember when I learned about that and feeling like Pokemon had lied to me. Water isn't weak against electric!
I love electroboom!

Electricity almost always transfers through the air and along the surface of materials. Air is considered an insulator because it doesnt conduct electricity very well, but it essentially acts like a very, very large valued resistor.

Given the voltage, you can calculate the distance through air a spark can jump using the breakdown threshold for the air. This is the distance at which the air breaks down creating a lower resistance path which lets more current flow, resulting in a large spark. For AC wall voltage this distance is extremely small, and even 100% saturated air will still have an extremely small spark distance.

In other words the humidity isn't directly a problem. The problem is condensation and corrosion, which could result in shorts, fires, and shocks, as well as electronics which fall into water or have a loose wire inside. Hair dryers, curling irons, etc can be dangerous because their heating elements can have live wires inside that could shock you if you dipped it in water. GFCI is meant to save you in cases like this by turning off the outlet.

That is what I was wondering, I had never heard of the humidity being a problem in bathrooms but, I also had never deliberately tried to make an almost sauna/steam room state in a bathroom either.

Not on its own. You'd have much more of a risk of shorting out because the water condenses on all the surfaces.

Pure water is a fairly poor conductor, and the ions that make it conductive don't always follow the water into the air.

You can force it to be conductive by using a high voltage current, but a high enough current will make anything conductive, given enough power, so that's probably despite the point.

Short of super-saturating the air, it's probably difficult, if not impossible to make it inhospitable to breathe in with eager vapour. Water can only hold so much, and while you can increase the amount it can hold by changing the temperature, you'd be overheating the the traditional way at that point.

Maybe some extreme super-saturation of the air, so the water condenses in the airways? Although that's extremely unlikely, since it'll probably condense on the rest of the person, and the available surfaces first.

That last sentence is a scary image to think about, but yea I can see the process on it. It would condense on the person prior to the air in the lungs, but if it didn't..yikes

Someone DM William Osman.

Check Michael Reeves hasn't already done it...

As said in another comment, with high enough voltage, it's all conductive.

That said, in the space of a whole room, there's a lot of things going on. The electricity is trying to find the most effective single path to ground so, once you get to a voltage that can travel through the medium, it then has to navigate the entire room for that path, going through resistance at every point. By the time the charge gets anywhere, it will have been diminished to nothing. Also, paths and resistances will change unendingly due to temperature, dewpoint temperatures in air pockets, airflow, the content of the air that isn't water or air itself, etc.

Technically, being INSIDE water is being at maximum humidity so that personally counts for me.

I can think of a few things to point out here:

water itself does not conduct electricity, it's the ions present in an aqeous solution that transfer charges. So humidity itself would be pointless in a case where the water droplets don't have charged ions present inside them.
even if the droplets do have charged ions present, those ions would still need a way to transfer charges between those droplets through the air. That is only possible if either the air is too hot (basically plasma) or the charge density in the droplets is too high (essentially lightning, albeit a little different).
another possibility for something like this to happen would be droplets condensing on exposed circuitry. If there happens to be live wires getting exposed through the walls, under the switches, or in an appliance, any droplets that get condensed at those spots would start conducting electricity (dust often has enough salts to allow such contaminated droplets to conduct electricity, but don't quote me on that). Do note that the atmosphere in the bathroom would still be safe, it's only the wet regions of the bathroom, like the floor and walls, that may conduct electricity.