You can make Firefox create an automatic HTML backup (bookmarks.html) when you exit Firefox if you set the pref browser.bookmarks.autoExportHTML to true on the about:config page.

That backup is created by default in the profile folder as bookmarks.html, but you can set the file name and path via the pref browser.bookmarks.file on the about:config page.

Note: an HTML backup doesn't preserve tags and annotations, so you lose those if you need to import the HTML backup.

See also http://kb.mozillazine.org/Export_bookmarks

You can't set the location of the daily rotating JSON backups. Those backups are always created in the bookmarkbackups in the Firefox profile folder. You can specify how many JSON backups are kept via the pref browser.bookmarks.max_backups (5).

Thank you cor-el. That information is welcome. I use a Linux OS. The path is /data/data/current/firefox/bookmarks.html Is it possible to specify the date as part of the file name?

I should have made it clear that I wanted Firefox to remember the folder I have been using via Bookmarks Organiser to hold json backups. It seems there is no setting I can use for that.

You can't specify the location of the bookmarkbackups, so I offered the HTML solution.
You can't modify the name of that HTML backup to include the date or you need to modify that pref each day to update the name.

On Linux it might work if you create a symlink of bookmarkbackups to another location, but I've never tried that myself.

Thanks cor-el. The reason I export the bookmarks to a json file is that I have a folder for bookmarks which I back up. Having to navigate to that folder is no great hardship but I was hoping I could get Firefox to remember the location as it does for downloads. The bookmarks organiser opens the save dialogue to my Desktop folder; I was hoping to change that somehow. There is an extension that may help but it would be overkill for me.

Thank you very much for your help.