There are articles for that, just upload the backup file or backup the whole profile and "ship" it with you.

• Export Firefox bookmarks to an HTML file to back up or transfer bookmarks

AND

• Back up and restore information in Firefox profiles

See also:

• https://support.mozilla.org/kb/Recovering+important+data+from+an+old+profile
• http://kb.mozillazine.org/Transferring_data_to_a_new_profile_-_Firefox

If you use tags in your bookmarks, make sure to back up a recent .JSON file from your bookmarkbackups folder (or create a fresh backup). The .HTML export is an older format that is cross-browser compatible, but it doesn't include the tags.

To get the bookmarks from the .JSON file to your new Firefox, this article has the steps: Restore bookmarks from backup or move them to another computer.