First a disclaimer and some assumptions regarding your setup. I have used these instructions to get a working disk on my setup - but this does not mean that the same steps will work for you, so use caution - and if anything goes wrong please feel free to add to these steps.
I am also assuming that you are using the latest operating system patches for OSX and I'm at version 10.7.2.
Step 1 - Connect and prepare your external USB drive.
Connect your USB disk and open disk utility.
Select the format for both of the partitions as Mac OS Extended (HFS) and click apply. Note - this will erase all of the data from the selected drive so make sure you have the right drive selected.
Step 2 - Download and Install the OSX recovery disk assistant from Apple - http://support.apple.com/kb/dl1433
Step 3 - Open Time Machine preferences and click select disk. Select the TIMEMACHINE volume. Also check off the encryption checkbox to ensure that your files are protected. You will be prompted for a passphrase to use for this. Note - this is a different passphrase than is used for the user on the computer and for the wholedisk encryption you have on the hard drive.
Step 4 - Wait until the first backup is complete. Once the files are transfered for the first time the backups will be encrypted as well. This also will take some time. During these operations you can eject the disk and have it resume once the disk is reconnected. When you reconnect the encrypted disk, you will be prompted for you password.
Step 5 - Once the backup and encryption operations are complete, you should test your backup solution by rebooting the computer and holding down the Option key, then select the USB disk. The recovery wizard will walk you through the processes of restoring your computer from the recovery Volume on the USB drive.
I will update this post, when I get a chance to test out the recovery process.
Step 6 - Always remember the rule of 3 when making copies of your important data. 1 live copy, 1 backup copy, and 1 copy stored somewhere other than your other two. In this case you could get by with just periodically (weekly / monthly) backing up to the USB drive and then storing this drive in a different location.