You can connect your YouTube channel to either a Google+ Personal Profile or to a Google+ Page. In general, the latter is the preferred solution.
To connect to a Profile, see https://support.google.com/youtube/answer/2657961?hl=en
To connect to a Page, see https://support.google.com/youtube/answer/2897336?hl=en
Once you have done this, you can make a video private and share it to one of your circles through the Video Info Edit page.