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That's probably meant to be Mrs. Charles DeLoosey Oelrichs, a prominent member of Newport society and a member of the Congressional Union for Woman Suffrage too. She married Charles DeLoosey Oelrichs (1882-1973), a stockbroker, in 1907, and they were divorced in 1921.

They had one child, daughter Margery (aka Marjorie, aka "Bubbles"); maybe that's her in the photo. If it is, she eventually married Eddy Duchin, the bandleader, in 1935, and became mother to Peter Duchin (b. 1937). Marjorie Oelrichs Duchin died two days after the birth of Peter.
en.wikipedia.org/wiki/Marjorie_Oelrichs
en.wikipedia.org/wiki/Eddy_Duchin
en.wikipedia.org/wiki/Peter_Duchin

The Mrs. Oelrichs in the photo above does not appear to be the same woman who, in another Bain/LOC photo, also is identified as Mrs. Oelrichs. Perhaps Bain made an error in one of the identifications. Moreover, the daughter in the other photo (who does not resemble the girl in this one) is identified as "Margaret," not "Marjorie." Here is the other photo:

Indeed, Wystan, this woman and daughter look more like the mother and daughter in the pictured labeled as Mrs. Amos Pinchot.
www.flickr.com/photos/library_of_congress/4037482176/
The daughter, in particular looks to be wearing the same hat.

www.newyorksocialdiary.com/node/136306
has pictures of Gertrude Minturn Pinchot that look like this woman, but is mainly about her daughter, who was the actress Rosamond Pinchot. Pictures of Rosamond as a girl on the web page could certainly be this girl.

The Oelrichs seem like a complicated family with a lot of same-named people; Margery/Marjorie Oelrichs, daughter of the Charles DeLoosey Oelrichs, was born after 1907, which would seem to make her a little younger than this child.

I like the alternate identification--they do look much more like the Gertrude and Rosamond Pinchot in the photo swanq links to. Not only the same hat on the girl--looks like it could be the same dress, socks, and shoes too!

Probably Vincent Astor, en.wikipedia.org/wiki/Vincent_Astor, the "richest boy in the world" given his inheritance when his father died in the Titanic disaster.

Another Bain/LOC photo from this sequence: www.flickr.com/photos/library_of_congress/4036736337/in/p...

swanq and Wystan: Thanks for the additional information. We'll add it to the record next time we update.

China and glass shop, left of center: DAVIS COLLAMORE & CO., New York Est: 1861

Intelligent use of awnings.

Another Bain/LOC photo appears to have been taken on the sidewalk outside the Newport Casino's shops:

That building is now the International Tennis Hall of Fame on Bellvue Avenue. I passed it a few months ago while visiting Newport. I recognized it immediately. It still has the canopies, cedar shingles and that rounded archway.

Nice work Richard! Times sure have changed...