The wines are in two locations, their country place near Gettysburg, Pennsylvania ('Copper Top'), and their home in Washington, DC ('Georgetown').
You can see the list in its original typewritten form, complete with notes such as 'signed by a bunch of journalists and Carter administration people', which apparently applies to a bottle of Ch Haut-Brion 1969.
Download the list here.
In the picture, Betsey is holding a copy of Johnny's last, posthumous book, Far Flung and Well Fed. See more in A day of glorious bottles.
And here is a link to a 2 Jan interview with Betsey on National Public Radio.