Can I set when bookings for classes open?

Yes, if you want to prevent people booking a class until a number of days before the class starts, you can do this with the "Schedule when bookings open" option in the class schedule settings.

Find your class in admin dashboard and edit it

Click on the Schedule tab

Scroll down to "Schedule when bookings open" and tick the box. You will then see two new options appear: the number of days before bookings should open and the time at which they should open

When someone tries to book your class before this time they will get a message saying that booking isn't yet open for this class.