The plate is going to surprise you, but first, we have to do a little triangulating on this one. There are many mentions of the chapeau bras in La Belle Assemblee for 1814 because once again Mrs. Bell claims to be the inventress of the Ladies Chapeau Bras and wants to advertise them.

In LBA, several mentions here (though no plates): https://books.google.co.uk/books/reader?id=88sRAAAAYAAJ&printsec=frontcover&output=reader&pg=GBS.PR4#v=snippet&q=chapeau%20bras&f=false

The August 1814 Fashion descriptions include the “Circassian Ladies Corset and Sea Side Bathing Dress” which also adds: “Head-dress Chapeau Bras” 
Circassian Ladies Corset and Sea Side Bathing Dress, August 1814
https://georgianera.files.wordpress.com/2019/04/circassian-ladies-corset-and-seaside-bathing-dress-fashion-plate-from-la-belle-assemblc3a9e-or-bells-court-and-fashionable-magazine-sparc.jpg

And there is the
Ladies Chapeau Bras and Full Dress…April 1814
https://tessa.lapl.org/cdm/singleitem/collection/fashion/id/423/rec/6

These examples look more like a calash and indeed that is how the author envisions them in The Ladies Monthly Museum, April 1820, in an article describing female fashion from ancient to modern: “a cardinal and calash..a cloak…a kind of hood; it was very large, and could be worn over the hair in full dress because it was kept in shape by runners of cane; its appearance was not unlike the modern chapeau bras; but all those who have ever seen both must acknowledge the former was far inferior in elegance, comfort, and convenience, to the latter. (p.197-198) https://books.google.com/books?id=xFpEAQAAMAAJ&pg=PA197&dq=chapeau+bras+%22ladies+monthly%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwiMq6GGvr3nAhUlvFkKHVppDa8Q6AEwAnoECAMQAg#v=onepage&q=chapeau%20bras&f=false

La Belle Assemblee mentions it again in 1820 (p. 182 in “Cabinet of Taste” article), saying that the “mantles of grey, or violet colored sarsnet, are much worn, they descend as far as the heels, and have hoods drawn with ribbon, stiffened with whalebone; which latter improvement, to be Candid with you, is, I think, an awkward imitation of Mrs. Bell’s Chapeau Bras.”