Hi there gwennie_bean,
Bedtime is no longer a supported feature in iOS 16:
The Bedtime feature is available only on iOS 13 or earlier. If you're using iOS 14 or later, learn how to track your sleep on Apple Watch and use Sleep on iPhone.
You'll find this information here: Use Bedtime - Apple Support
With that said, you'll want to be sure you have your Wake-Up Alarm set for your full schedule with the steps below:
Update your full schedule
1. Open the Health app and tap Sleep.
2. Tap a schedule in Full Schedule & Options.
3. Tap Edit under the schedule you would like to update.
4. Tap the Days Active and drag the curved slider to set Bedtime and Wake Up times. The slider turns orange if the schedule does not meet your sleep goal.
5. Tap Alarm to turn on an alarm and adjust your alarm sound, volume, and haptics.
6. Tap Done to save your changes.
You can also turn off your sleep schedule as needed. In the Health app, tap Browse > Sleep > Full Schedule & Options. Then tap Sleep Schedule at the top of the screen to turn your schedule off or on.
Those steps can be found in the 'Update your full schedule' section of this support article: Track your sleep on Apple Watch and use Sleep on iPhone - Apple Support
If you have your Wake-Up alarm set up properly and it's still not sounding as expected, you'll want to reach out to Apple Health Support directly. They're best-equipped to help. This link will help you get started: Apple Support
Take care.