I kept the washcloth inside my bra all the time. I would get it very wet, wring it out slightly so it didn't drip and them put it inside my bra all day long. It would dry out after a few hours so I would rewet it, if home. If not, I had to wait until I got home, but it was always there. I wore a runner's bra to bed with the washcloth in it too.
I wore it to work too! I waitress and tend bar so I had a vest that covered my chest so it wasn't noticible. If going out, I tried to find something to wear that allowed me to keep the wash cloth on, but if not, I just went without.
Hope that helps.
FYI, I also had a rash come out on my chest while doing this. I think I was killing off some fungus or bacteria hibernating there.