Q. How do I export my references and bibliography in MS Word to RIS/BibTeX?

If the references in Word was created using a Reference Manager tool like Zotero or Mendeley, the data is already in structured format and you can extract them using the free Reference Extractor tool with almost 100% accuracy. 

Similarly if the references were created with Word's build-in reference function you can follow the procedure here to extract them. 

However if the references were created manually by hand then you will need to use various tools to parse your plain-text bibliography or references into BibTex format that can then be imported to reference management software, Do note that these tools are not 100% accurate, depending on the citation style used.

Tool #1: AnyStyle.io

1. Make sure each of your reference entry starts in a new line
2. Paste the bibliography into the text area.
3. AnyStyle will parse the entries. If you notice any items labelled incorrectly, click on the item and click Assign label and choose the correct one.
4. Save it as BibTex file
5. Import the BibTex file to your Zotero library.

Tool #2: Scholarcy Reference Parser

1. Make sure each of your reference entry starts in a new line, and click Convert
2. The BibTex will appear on the field just below the text area. Select all of the contents of the BibTex and copy them (Ctrl + C)
3. Go to Zotero and click on the folder where you want to import the entries
4. Click File >> Import from Clipboard. This will paste the BibText entry from earlier to your Zotero library.

If these methods do not work well, or you need to do this process in bulk please approach the library for assistance.