You can't invite Public to a Hangout on Air (HOA)
"You'll be prompted to invite your friends or circles before you enter the Hangout On Air. Please note that you can't invite the public to join a Hangout on Air but, you can open the broadcast for public viewing by clicking Start broadcast from within the Hangout On Air window."
You can invite them to watch the video in YouTube: Get the link already before you go On Air:
You can also make an Event on Google+ and share that link to Facebook already before the HOA time: Just make sure that those you are inviting have you in Circles, too.
FAQ about Hangouts on Air
Video: How to create an Event and add Hangout on Air