Hello Vicor,

Please note that our support agents are unavailable on weekends.

The reason why the form is not visible for non-logged-in users is not in Amelia, but instead in your security settings. They're either configured in a Security plugin (if you have any), or they're on your server's side. 

The best option would be to reach out to your hosting provider, send them the link of the booking page and tell them exactly what you told us - you can see the page when you're logged in as an admin, but you can't see it from an incognito window (or when you're logged out). They should be able to lift the block, so admin-ajax calls are sent for non-logged-in users also.