I believe that it was $1.25 or $1.75 last year in September, I'm not sure which but still fairly reasonable compared to other parks like Yellowstone/Grand Teton. You cannot use cash, you need to go to the camp store and buy tokens (if you are staying at Swiftcurrent cabins you get a free token for each day). The tokens are good for 8 1/2 minutes of water and they do shut off without warning at that point. If you need a long shower after a tough or cold hike I would recommend having extra tokens. The water pressure and hot water is very good and at least when I was there in September they were also very clean for a campground shower. You do not get a towel.
Also, the temperature controls are set in the reverse direction compared to most showers. I kept thinking there was no hot water. It took me a couple of times to figure it out!
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Thanks. The price is very reasonable in my opinion. We will be camping July 5-7 at Many Glacier. So I need to pack some towels, warn everyone about the controls and have them practice an 8 minute shower.