Hello!
This is a difficult citation because it's out-of-the-ordinary.
You've accomplished step 1 - adding the document to Zotero.
Sometimes the web site will provide the information necessary for Zotero to identify the type of document to cite it. If the web site doesn't, then you have to provide that information to Zotero yourself. You are correct to identify it as a "document". This is important because to cite any source correctly, you must first correctly identify it. Zotero provides lots of options when identifying a source. To see these, click on "item type" in the Info space on the right side of the Zotero window.Once you choose the item type, Zotero will provide you with the needed boxes to fill in.
Refer to the APA Manual p. 205, 7.03 Technical and Research Reports for examples of the format most often used for documents on the web. The next box to fill in is the title of the document. Be sure to capitalize the title as you want it to appear in your reference list.
In the Info space on the right side of the Zotero window, click next to the word "Title" and type it in.
Next is the author. Using the rest of the web site, specifically this page: http://www.romecriteria.org/criteria/, I identified the author as the Rome Foundation. I then added the URL. According to the Manual, the only other information needed for the citation is the date. Since it is not on the document, I leave it blank. Zotero will fill in the date as (n.d.).
It looks like this in Zotero:
This information yields a citation of (Rome Foundation, n.d.) and a reference entry like this:
Rome Foundation. (n.d.). Rome III diagnostic criteria for functional gastrointestinal disorders. Retrieved from http://www.romecriteria.org/assets/pdf/19_RomeIII_apA_885-898.pdf
I "know" this information comes from the book, but the web site doesn't make that clear in the way the information is presented, so I'm not comfortable with citing it as an ebook. That's why I chose the web document format, as you did.