Zotero offers plugins for Microsoft Word and OpenOffice, which you can download from Zotero's website. These allow you to easily cite items from your Zotero library in your papers and generate footnotes in Bluebook format.
Once you've installed the Zotero Add-In for Word on a PC, when it comes time to cite click on the Add-ins tab, and select "r2" from the Zotero Custom Toolbar. (Please explore all of the icons in the custom toolbar!)
On a Mac, it the Add-In is located here:
Inserting a citation with Zotero (for an article in your Zotero library with "We", in the title, for example) while writing looks like this:
Because you've already stipulated the Bluebook style as your default, the footnotes appear at the bottom of the page in Bluebook format!
Zotero has put together a video tutorial on how to create citations using Zotero and Microsoft Word.