How to open time machine progress bar window
I am 100% sure there is no way to see how long the the backup takes just the size of the backup and how much portion of the size it has already backed up like shown below.



The only time duration that Time Machine shows is when you are restoring from a backup and during the first time you set up Time Machine using a empty hard disk.

I just noticed that "Open Time Machine Preferences" shows a progress bar for the current backup operation. I just upgraded to Maverick recently so this may be a new feature.