Firefox bookmarks are not automatically backed up with User Data.  Follow this guide to manually back them up.

Step-by-step guide

In Firefox:

  1. Press the "ALT" key to bring up the Firefox Menu at the top of the browser.
  2. Choose the "BOOKMARKS" item.
  4. A new window will pop up.  At the top of the new window, click the "IMPORT AND BACKUP" button.
  5. In the menu, choose "BACKUP".
  6. A new window will pop up.  Navigate to your DESKTOP folder and save the file.  Keep the default name (example:  "bookmarks-2015-03-05").