Nolan, two things:
1) With backup frequency set to 'Every time..' (Edit > Catalog Settings > General tab) just close and reopen the catalog. You'll be asked if you want to backup.
2) There's nothing 'special' about Lr's internal backup routine. It's just a copy of the 'catalog-name'.lrcat file. With Lr closed, you can make your own backup copies using Explorer or other copy/backup/sync tools.