sci-fi short story set on the moon, flying in no-gravity hall, possibly 70s?

I read this in a sci-fi anthology some time in the 90s, but it was definitely older than that (I can't remember any other story in the anthology, but in any case this was a French collection of translated stories, so I doubt it'd help).

As far as I remember, the story was set in the future on the moon, where a colony had been established under some sort of glass dome.
I think the main character was a teenage girl/young woman, and she went to this sort of public flying room where there was almost no gravity and people could fly around and do tricks, a bit like a futuristic ice rink with flying instead of skating.
There was some kind of column of rising air you could ride to the top of the room to float back all the way down.
There was, I think, some kind of accident while she was flying, and she was rescued by a better flyer who lectured her about being reckless.

I'm fairly sure the entire story was centered around the flying, but I might be wrong.

Anyway, if anyone has read this, I would really appreciate a title or author name, or a collection in which I might find it again.

Thanks in advance!

Hmm. I know I've read this story. I thought it was in one of the Asimov/Greenbaugh/Waugh sets, but apparently not.

Girl meets boy on moon, where they go to a lunar playground of sorts involving wings and hang-gliding. I'm pretty sure the girl ends up with a broken arm. I know one of them is a lunar resident, but not sure which.

Maybe it's a Zenna Henderson short story?

Perhaps The Menace from Earth by Robert Heinlein from 1957.
Here is part of the description from http://www.spacefuture.com/tourism/sciencefiction.shtml
A good place to start seems to be Robert Heinlein's wonderful 20-page story "The Menace from Earth", first published in 1957 by Fantasy House Inc, and more-or-less continually available in one or other edition of a short-story collection of that name. It's about a 15 year-old school-girl, Holly Jones, a 3rd-generation lunar inhabitant, whose hobbies are designing star-ships and flying in "Bats' Cave", a natural cavern two miles wide and half-a-mile high which is Luna City's air reservoir and is also used for recreational flying. (With weight 1/6 of that on Earth, almost anyone can fly like a bird on the Moon.)

The story concerns a rich tourist from Earth, Ariel Brentwood, who temporarily mesmerizes Holly's boyfriend, Jeff Hardesty, to Holly's discomfort. The heart of the story concerns Holly helping Ariel to try out flying in "Bat's Cave".

The Menace from Earth is the one I was thinking of. Hopefully it's what alloutofwords wanted too. :)

Ah, yes, that's it! Thank you very much.
I didn't remember anything about the boyfriend or the other woman.
This was one of the first sci-fi stories I read as a child and it was the one that drew me into the genre, I was despairing to find it again.
Thanks again!