Not only can I describe what a 15th century backgammon board would have looked like, but ...
The photo above is a game board inlaid with ivory and chestnut, c. 1500; it's got a chessboard on the other side. (See Gary Halstead's photographic tour of the woodwork at the V&A for more information.)
There are other examples of similarly ornate game boards from the 15th century, lest you be thinking, "Oh, Karen, it's lovely, but it's far to late for me."
The Musée National du Moyen Age has a fancy game box, made of ebony and dyed walnut, which has six sliding boards (checkers/chess, nine men's morris, fox & geese, trictrac, glic, and one I'm not sure about); it dates to the 15th century. (I would theorize that, based on the level of craftsmanship in this game box, it was an item of some expense, and that the owner of this must have been rather wealthy; perhaps it is not too much of a stretch to think that a noble lady might have played some of the games in the box, though the presumed expense and craftsmanship of an item of course does not directly imply ownership or the social status of the owner.)
I can't positively say that ladies would or would not have played backgammon/tables in the mid-15th century. Alfonso X's Book of Games features a section on backgammon -- libro delas tablas -- which includes an illustration of two ladies playing backgammon. One of the illustrations in the Manesse Codex (c. 1300-1330) -- specifically, that of Herr Goeli -- depicts two gentlemen playing backgammon. An illustration in the Luttrell Psalter (a bit later in the 14th century) shows a man and woman playing backgammon in a garden; the fact that he wears a crown, and she wears a gossamer veil, lead me to think that these are supposed to be persons of some rank. But I have no documentary evidence for mid-15th century specifically.
I should also note that "tables" may have a broader meaning of a board game in general (including backgammon) and in some cases included games involving gambling. See references to a gambling house in which the games are fixed (1375-76) and gambling and cheating (15th century).
If we are to take period imagery as evidence of what ladies would have played, then perhaps chess would have been appropriate as well. There are 14th century ivory mirror cases -- such as the ones at Cleveland Museum of Art and the Louvre -- which feature couples playing chess. In the Manesse Codex, Markgraf Otto von Brandenburg plays chess with a lady. And there's an illustration of a man and lady playing chess in a copy of La belle dame sans mercy (The Hague, KB, 71 E 49) from France, c. 1470-1480.