You'll probably find a small 28 back is fine. Bravissimo is your friend. Dd has been a bravissimo girl from the same age and size. Go and see them rather than ordering on line . If you must go on line I suggest panache tango 2 balconette ( the plunge is pretty plungy) tbh it's the best fitting bra dd ever had - she's had a succession of sizes and occasional other styles but always come back to that one.
Never ever take her to m&s! Not only will you get a bad fitting but stupid thoughtless comments like " you shouldn't be in under wires at your age " ...." You can possibly be a 28dd..... Oh you are.... Try these 30Cs instead as we haven't got the right size"
Fortunately dd is a tough cookie but she could have been really crushed by them.
I got DD some from M&S today. They didnt even ask if she wanted fitting - I just went into the changing rooms with a couple we wanted to try. They didn't question anything we took in with us, nor any comments either way.
I think generally so long as you are happy to decline their fitting service they will leave you to it.
We tried a few places today and the bras we chose were from M&S as DD liked them best, they had the size we needed and they fit well.
Could you take a 28 inch in a little bit? I can see why you wouldn't like underwired... I don't even like putting DSD (also 10) in a slightly padded bralet her mum had got before she moved to us. So I got her some crop tops, though she's less than an a cup, though you can see little peaks. But wow... I can really see what a problem your having are there websites where you can get bespoke bras?
We tried the 28" back at M&S today and it seemed ok. She says why she tried on wasn't comfortable under the bust, not tight around just not nice. I would never let a fitter near her in there It did seem to fit ok, she was filling the cup but not spilling over IYSWIM.
I don't see the problem with wire tbh, but we had a massive row with her DM last year about it. She doesn't wear wired bras and doesn't feel DSD should either.
The nearest Bravissimo store is an hour away, a bit of a trek if it turns out they don't have anything to fit her, maybe I'll call them.