I have received invitation almost as soon as Google made this public (from my university senior Arif bhai, who is working at Google). And I am quite enjoying after two days coz now I see lot of known people coming here at least to try out. Want to invite others but don't see invite option? You can easily send invitation to your friends with gmail accounts.
1. Write something to share. You can just write - Click on "Learn more about Google+" to join
2. Click on "+Add circles or poeple to share with..." and write down there Gmail addresses
3. Click "Share"
You may see a warning that people not already in Google+ will receive the post via email. Actually, thats what you want so no worries :)
Original post here. I tried to make the process simpler. Let me if anyone needs invitation!