It's been quite a few years since I needed to do laundry in Yellowstone, so no idea how much it costs now. When we were in Monument Valley recently, the (one and only) CG washers were $3 apiece, which is pretty pricey. I'd expect something similar in YNP. Like Old Biscuit, it's not been a big part of our travel budget, just is what it is.
In addition to any laundry facilities at Fishing Bridge, there are some washers & dryers at Lake Lodge, not far away. Not a large laundry room there, just FYI.
2020 Toyota Tundra CrewMax 5.7L V8 w/ tow pkg, Equal-i-zer
2020 Lance 2375