If you have timeslots that are displaying as "manager only booking" this is because a manager's login is required to override one of the advanced settings that are in place for that timeslot.
These timeslots go against your settings in place so they could have a shorter stay time for the customer that they need to be made aware of or it could be that you have reached the max covers at that time.
Manager only timeslots can only have a booking added by an Owner/Manager login and these timeslots are not shown on the online widget.
Here a couple of examples why a timeslot would be manager only -
If your table turn time conflicts with your close time in the opening hours setting, bookings that have a shorter stay time than the default table turn will require a manager to override the stay time. This means the customer will not have the full stay time on the table so they need to be made aware of this. You can view our article here that goes into a bit more detail.
Max covers per timeslot have been reached but you still have tables available. A manager override will allow further customers to be added to that timeslot.
If the setting preventing the booking at that timeslot is no longer applicable going forward, all you need to do is remove the edit in the specific setting.
We have an article here that lists all possible causes of why you can't add a booking to the diary or grid view, and another here that lists why you can't book via the widget. They are great articles to use for troubleshooting when you might not be able to quickly find the setting that is preventing bookings.