hello maryjanekitten069, firefox sync was not primarily designed as a backup service but to keep multiple devices on the same level (therefore the name firefox sync).

in order to access the data in your sync account you'd need three components: the username, the password & the recovery key generated during the original setup of the account.
in case you have all those three pieces of information available, you can go to firefox > options > sync > set-up sync > i have an account > i don't have the device with me in order to link firefox to your existing account.

It is best to create a backup of the bookmarks yourself.

Firefox keeps rotating daily JSON backups of the bookmarks in the bookmarkbackups folder, one for each day that Firefox has been started up to a maximum of 10.

• Bookmarks > Show All Bookmarks > Import & Backup > Restore > Choose File

• http://kb.mozillazine.org/Backing_up_and_restoring_bookmarks_-_Firefox