Unfortunately, almost never. There is a co-op about an hour away from me - and it's not 100% zero waste or anything; still many pieces of packaging throughout the store - but they are trying to promote bulk and they're in a small kind-of college town. Unfortunately super expensive (or should I say, accurately-priced?) as well and obviously you need to have a membership. I applaud them, still.
I think a lot can be purchased close to zero waste without these stores, though, if you have the good fortune to be able to buy a lot at one time/stockpile when you find an item you need and work from there. I'm also interested in how this works out if say, me and a bunch of my neighbors got together to buy bulk online and split everything versus say, 6 households traveling around, buying 6x the packaging, to find items that we all use & need. Or 20 households? I guess a mini co-op is what I'm after. The ugly truth is that some zero waste stores may still use a lot of packaging anyways, just behind the scenes so you feel good about your purchases there.