O Cindy, this is a little treasure, but I hate to be the bearer of bad news (however you'd hate it twice as much if I gave you false hope) this print is not worth nearly as much as the appraisal says it is.
Let me explain what you have exactly, and sorry if it's a little complicated, it is.
This is a print taken from a book called La Vie et l'Œuvre de Pierre-Auguste Renoir ("The Life & Works of Pierre-August Renoir") published by a renowned art dealer of the day, Ambroise Vollard, Paris, in two first editions in 1919, just a few days after Renoir died. One was a print run of 100 on one particular type of paper and the second was a print run of 375 (yours) printed on different paper called Vélin d'Arches, a smooth cotton paper used for illustrated book printing -part of a total run of 1000. Here's what the whole book looks like. This one is being offered for sale retail for $14,000, which is a high price for one of these, $10,000 would be a more plausible upper end. it includes one original Renoir etching and 51 engraved plates of which yours may be one of those 51 but it could also be part of the remaining 625, printed on the same type of paper, but not one of the 375 numbered copies. One cannot tell because it was the books that were numbered, not the prints themselves. So when the books were broken up to frame the prints, the proof of which edition they were from was lost forever.
The prints were "hand pulled" from copper plates beginning on Dec. 15 1919 exactly twelve days after Renoir died on the 3rd December 1919 after struggling with failing health for over a year. So that makes them posthumous prints, always considered not nearly as collectible as those made during the lifetime of an artist.
In 1986, Ambroise Vollard's heirs started reprinting the copper plates, some tinted by hand with watercolor. These prints have a facsimile Renoir signature in the plate and are embossed "A Vollard" in the lower margin -so they can be told from yours- but their existence -and in unknowable quantities since they are open (un-numbered) editions- has greatly diluted the "currency" of the limited 1000 edition prints from 1919. These "Ambroise Vollard Estate Collection" re-strike prints sell for about $100 - $200 each at auction -if they sell at all- there are a great number that are withdrawn unsold.
Yuur particular illustration is taken from a painting that Renoir completed in about 1909, called, "Female Nude Drying Herself" or "Apres le Bain" ("After the Bath).
In spite of what you may have read, he almost certainly did use a model for this one. You can see how carefully observed the details are, particularly the hand. But you are right, there is a series of bathers that he painted from memory, without models. Like this one. And you can clearly see the difference.
Despite there being a lot more of these prints around than is often admitted to, they nonetheless were technically very well done, using a type of printing called a heliogravure (aka photogravure) print. The process is the same principle as copperplate engraving, but instead of hand engraving, the plate is prepared by an elaborate photochemical procedure. The polished copper plate is first prepared with a rosin ground (to give the exceptional tonal range this type of printing captures) and then photo-selectively etched with acid to create an intaglio surface, that is subsequently inked, and from which the prints are then made or "pulled".
One great way of identifying a heliogravure print is, if you look at it under a magnifying glass, you won't see any screen pattern or little dots, unlike images printed using industrial methods such as offset printing or letterpress (newspaper) printing, so it almost looks like an original ink-and-wash drawing or painting.
The way these prints started appearing on the market, with accompanying official-looking "certificates of authenticity" (COAs) is interesting. Prints by famous artists such as Renoir, Picasso, Chagall and Dalí are often sold at "fun"auctions on cruise ships. The auctions are typically held when the ship is in international waters, outside U.S. jurisdiction, where the auction companies can employ legally and certainly ethically dubious sales tactics, in collusion with the cruise operators.
They are not exactly committing fraud because each statement on the COA is true on its own, they are just put together in a way deliberately to deceive and imply they are rarer than they in fact are.
So on yours, the matting & framing has been expertly done. One can clearly see the press lines of the print, too, which is important. The print on its own probably has an auction value around about the same as the modern colored ones, about $200 tops. Add in the nice frame and mount and you're looking at $150 - $300 at auction and a full retail/replacement/auction value of $600.
I do hope this is not too disappointing! And if you need further explanation on this, please don't hesitate to ask, it's certainly a minefield!