Having just run through creating a new encrypted backup in the last week or so, the repair disk thing didn't work for me.
I've only found two reliable ways to create a bootable encrypted backup, and both involve creating the Recovery HD partition:
* Install OS X to the backup drive
* Use Disk Center in a
CCC trial to create the Recovery HD partition manually (apologies for linking to a competitor)
Once that's done:
* Run SD as normal
* Boot off the unencrypted backup
* Use FileVault to enable encryption of the backup