Well I'm downloading iTunes bought movie to my iPhone 5 on 7.1.1 it's working quicker than iTunes download..
iTunes > more @ the bottom> Purchased> movies> hit the cloud link to download.
or open videos via search then look @ the videos that are available via iCloud - with the cloud icon in bottom right of the movie poster..
I leave "Show All Videos" off because I have hundreds of movies in iCloud.
With that off in the iTunes Store you get a "Watch" button but no download option. You can work around the bug by leaving the "Show All Videos" on.