A version in plaster painted to resemble terracotta was shown in the Salon of 1781, followed in the Salon of 1783 by a marble, usually identified as the bust in the the Wallace Collection, which is signed and dated HOUDON F.1782.
H.H. Arnason, in his study of Houdon, has this appreciation:
"[The Madame de Sérilly is] another outstanding example of Houdon's ability to commemorate the exquisite ladies of eighteenth-century France. Her face is one of great charm and mobility. The large, hooded eyes look out with an expression of rapt, even sensuous attention. The long, soft hair is modelled with particularly loving care; the upper arms and shoulders are wrapped in a flowing cloak, which encompasses the figure, acts as a base and extends in finished detail across the back. This is the consummate type of the late Baroque and rococo portrait of a noblewoman, presented with the decarative grace of an earlier time. She is almost an anachronism among the soberly dressed gentlemen who accompany her in the Salon of 1781. As she belongs to an age of elegance rapidly drawing to a close, so most of them seem to predict a more democratic, bourgeois, and perhaps less picturesque century."
Arnason, The sculptures of Houdon, 1975, p.58.
The relationship between different examples of the sculpture is a bit of mystery:
At the time when Arnason was writing (1975) two new marble busts had recently appeared on the art market in New York, both signed and dated 1780, in an almost identical style, although one, curiously, was stamped upside down. They differed from the Wallace Collection in details of drapery and "required more research" ( note 151, p.113).
One was acquired by the Art Institute of Chicago in 1995.
The primacy between the two sculptures is now in some doubt:
See particularly the comments and photographs of Bath antiques dealer David Bridgewater:
"Bust of Madame de Sérilly", English 18th Century Portrait Sculpture [blog] Post of 19.02.2018
Mr Bridgewater is of the opinion that the Wallace Collection bust is a studio copy and the Chicago bust, where the marble is whiter and less flawed, is the original. The London bust is also missing the bow on the front of Madame de Sérilly's dress. This view would obviously fit with the dates on the sculptures. The Chicago bust is also considerably larger, 89 cm in height as opposed to 62 cm.
The provenance for the Wallace Collection bust is given as: Auction at Theil (Yonne), c. 1864. Duc de Morny; duc de Morny sale, May 1865, perhaps no. 445; Richard Seymour-Conway, 4th Marquess of Hertford.
According to the US. "French Sculpture Census" site, an "anonymous, untitled treatise in the curatorial file" traces the provenance of the Chicago bust back to Mme de Sérilly herself:
1794, Confiscated by the Revolutionary Tribunal [see anonymous, untitled treatise in curatorial file]
1796, Reclaimed by the sitter, la comtesse de Pange [see the same anonymous, untitled treatise]
Passy-sur-Yonne, by descent to the heirs of la comtesse de Pange [see the same anonymous, untitled treatise]
The bust was subsequently acquired by Nathaniel de Rothschild in 1899.
The logical inference seems to be that the the Chicago bust was owned by the Sérillys, and the Wallace Collection one made by Houdon to exhibit in the 1783 salon?
To complicate matters, a third example - presumably the other bust mentioned by Arnason - was donated to the Minneapolis Institute of Art in 1975. It is described as signed and dated on the bottom of the base HOUDON F. 1780. Again this looks to be pure white and the size is given as 87.6 cm x 61 cm. An expert from the Chicago Institute of Art specifies that the Minneapolis sculpture "appears to be a workshop example based on the Art Institute's bust", but does not say why; no-one, I think, is terribly certain.
"Portrait of Madame de Sérilly, 1780", Minneapolis Institute of Art.
Entry on the French Sculpture Census
Ghenete Zelleke, Notice in Art Institute of Chicago Museum Studies, Vol. 28, No. 2 (2002), p.86