I’m just imagining a business in the Nevada desert with a freight elevator that goes all the way down to the pool 
What is the deepest possible distance where it would be safe to wear normal swimsuits/bikinis?
After you’ve been down at the pool and returning to the surface and the bright sun would most likely be pretty memorable/unpleasant.
Try imagining it in Alaska, Siberia, or northern Greenland instead. Or one of the dry valleys in Antarctica. Because the Earth is an oblate spheroid, you won’t have to dig so far.
I’m not sure what the swimming pool angle adds to your question but the earth’s geothermal gradient, in the crust and away from tectonic plate boundaries, is about 25 °C per km of depth or 1 °F per 70 feet of depth.
I believe one can not withstand water temperatures more than 45 °C for long, due to the high conductivity of water so that would make your max. swimming pool depth at around 1800 meters. Even at 45 °C I don’t think you could stand more than a few minutes in the water.
This is ignoring the issues of needing ventilation so ensure you have enough oxygen to breathe and can get rid of the carbon dioxide you produce.
And note that this does not depend on what (if anything) you are wearing in the pool - unless, of course, you are wearing insulating clothing with a refrigerant of some kind inside.
No more so than stepping out of a movie theater at matinee time. Dark is dark, and you can’t get any darker than complete darkness. And the pool would probably have artificial lighting much brighter than a movie theater, unless you wanted the dim light for ambiance.
If you’re into geological scale engineering, you could start by surrounding the Litke Deep with walls and pump out the water.
Without air conditioning, the TauTona mine in South Africa (2.4 miles deep) would stabilize at 140F (60C). Presumably a swimming pool at this depth would also stabilize at this same temperature. That’s pretty freaking hot; the [url=Google]safest max temp for a hot tub is just 104F (40C).
Unsurprisingly there’s an XKCD for that.
(TL;DR -> depends on heat reserviors like magma chambers or heat-generating activity sub-surface such as tectonic movements as to depth possible.)
Not disputing you, Quartz, but wanted to use your point of where you dig down (in Nevada or anywhere on Earth). I am referring to the sub-surface geologic activity and/or structures that may generate heat. Stuff that makes mountains/volcanoes, lava flows, or other means of inner-earth heat escaping towards surface. Quartz’s mentioned areas have plenty of past and/or present histories (afaik) of high amounts of heat/pressure release from down below surface (not sure how to say it succintly, sorry).
I’m pretty certain that sub-surface temps around places like Mt St Helens (near enough to Alaska for ~relevancy to my quoting Quartz, I suppose) would be higher than sub-surface temps of a region like, say, Kansas or Oklahoma, where there is much less heat-producing geologic actions (afaik). And I’m positive that you would not need to go very deep under Yellowstone’s caldera to get into intolerable temp range as there is steam and super-heated gases escaping via vents in various areas of caldera and a fairly widespread area around it. I’ve enjoyed lots of hot springs all around Central/Southern Idaho that are directly related to magma chamber under Yellowstone 
Another good example of this is the Cave of the Crystals in Mexico where ambient temps can get to be mid-130’s F at depths of approx 1000’ below surface. This is due to a magma chamber’s heating it, of course.
Areas without magma chambers and/or tectonic activity (heat-generating process, per se) wouldn’t have as much heat, in general, at similar depths, in general, like the mine Machine Elf linked to just above. It would be relevant to know if Nevada has a large difference in sub-surface temps in one region -v- another of the State for thread subject.
No, you want the pool to be in darkness so the kids can’t cheat when they’re playing Marco Polo. Even more fun if the voices echo in the cave in which you’ve built the pool.
What about a private pool?
These details matter people.
Looking to join the Mile-low club?
You always need fresh air, so ventilation… so it all depends on how much you want to invest in ventilating to carry away the heat as well as maintain O2 CO2 and fart (etc) ratios.
The current record for a permanent construction is 2.6km under, the Gotthard Tunnel in Switzerland. Only brand new…
One thing though… 9 people died during its construction. Not sure where the engineers got the license to kill from… Borrowed it from 007 ? One or two might have been discovery of risks…
They seem to have taken the risk of boring through unknown rock… and simply hoping the rock overhead didn’t fall down … I don’t know if there was special attention to solving that… Seemingly the rate of boring was fast, like they took the risk of collapses.
Acording to Wikipedia, 1 person was killed by a rock, one person “was buried by excavation material”. Even those are normal constructions risks when doing building foundations. Although it’s not as dangerous as being a taxi driver, construction is certainly high-risk when compared to office work. But of course most of that risk is “working at heights”.
Actually, I haven’t seen the 90 year survival rates for office workers compared to construction workers… maybe it evens out at the end due to the hazards of a sedentary lifestyle?
The high Gotthard Tunnel, oppened in 1882, killed around 200. There must have been some rockfalls, but I doubt taht was the major cause of death.