You can lock your public page behind a code. Visitors who do not have the code see a prompt instead of your page.
Page access codes are part of Plus.
Setting one
Settings, Privacy, Access code. Pick something memorable but not obvious. We do not store it in plain text, only a hash.
Sharing the code
However you want: DM, email, group chat. Once a visitor enters the right code they get in and stay in for the session.
Removing it
Clear the field in Settings and your page is public again.