Currently, Bitbucket Cloud does not have a feature for users to take backups of their repository.
The method which users can use now is to perform a clone of their repository as a form of Backup.

Suggested Solution

Have a feature like a backup manage where backup of the repositories gets created and stored for a certain number of day. Users have the ability to download these backups when they would like to. The backups can be cleared or overwritten with new backups every interval of certain number of days.