When the waiter asks if they want dessert, he should also drop a card with URL/qr code to the app.
Depending on your flow, it will point to your landing page or directly to testflight (where they register to download the beta, you get their email also from here).

They key is to have real early adopters.
With this system, you:
- make it easy to discover the app
- give them a chatting/funny topic (will remember experience)
- have "true" adopters since they are at that restaurant

...might also suggest to snap a picture with a restaurant mascot for the picture they share related to their dining experience.