What were the physical dimensions (ie, waist, hips, bust, height,
shoe-size, etc.) of Elisabeth Amalie Eugenie, Duchess in Bavaria and
Princess of Bavaria (1837?1898) (also often called Sissi)?

I will need some documented references (this is to settle a bet.)

State secrets cannot be divulged here.
Here are some pictures of Sissi.  Looks like Romy Schneider was well
cast for the role.
http://images.google.com/imgres?imgurl=http://worldroots.com/brigitte/royal/gifs/sissi.jpg&imgrefurl=http://worldroots.com/brigitte/royal/habsfamily.htm&h=560&w=501&sz=45&tbnid=LpWXSyymhugQkM:&tbnh=131&tbnw=117&hl=en&start=4&prev=/images%3Fq%3Dsissi%26hl%3Den%26lr%3D%26c2coff%3D1%26safe%3Doff%26sa%3DN

Here is an Italian website that recalls that she suffered from
anorexia:  172 cm and 50 kilos:
http://www.ilcacciatore.com/schede/sissi.htm

This raises the question of at which point in her life do you want the figures?

There was an exhibition in Mannheim a few years ago that included her dresses:
http://www.sisi-net.de/news/news.php3?pid=22

The catalogue should have many photos.  Who knows, maybe someone in
the costume department knows the measurements of the mannequins used
to display the items.

Ditto perhaps for the Sissi exhibition in the Hofburg in Vienna:
http://www.hofburg-wien.at/en/site/publicdir/

Perhaps this is enough information to settle the bet, especially if
one of you thought that she was a buxom Bavarian  - or as they say
there:  "one with a lot of firewood in front of the house."

Good luck!