Lots of good advice, and as is probably now clear; "yes GBs do really exist"
But as mentioned in several of the replies, the best option is to find an established, safe, and reputable GB group/club versus trying to set a GB up ad hoc from a selection of random guys. Some couples may have more experience in setting up a GB themselves and thus have higher success, but for most it probably will end up as an exercise in frustration and disappointment for all the challenges mentioned earlier in the thread.
Our problem over the years was actually finding that magic "established and reputable" group!
When we lived in the SF Bay Area, there were several groups/clubs and is how we knew such a thing existed. Unfortunately we weren't yet really into trying a GB then, so we missed an opportunity.
When we moved to central NC and started to have an interest in GBing, we thought we'd just as easily find a group/club... but nope
This went on for years.
We then tried like other couples to find some guys to get together on our own, but that never worked out. And we talked to other couples trying the same, and they'd show up at the hotel to have most of the guys no-show or just generally not work out.
But about three years ago we finally found a nice GB group/club that we played with, but that now unfortunately I think is disbanded, and haven't yet seen another take its place in our area.
Based upon those observations, and the previous posts in the thread, the availability of these groups/clubs is going to be very regionally dependent, and that will likely be dependent on the size and maturity of the lifestyle in that area.
Regions like NYC, California, Florida, and other larger metro areas are just more likely to have these groups/clubs. So if one area doesn't, it may make sense to expand the search to the nearest large city.
...on that note, we're always looking out for another reputable GB group in the Triangle, Triad, Fayetteville areas