Calendar: Day 0 & Cycles

The school district where I work has special days set aside for staff, there are no classes or school days, and the staff attend professional development events.

On the calendar, these days are marked "0" (zero) and to the Day Cycle it's as if they didn't happen. For example:

Thurs Oct. 13th: Day 4
Fri Oct. 14th: Day 0, No Classes / Professional Development
Mon Oct. 17th: Day 5

Is there a way to enter that in the calendar? 

Sure. You have to configure your cycle for the full academic year first, as if this Day 0 days did not exist.
Once configured, from Menu > Calendar > Right click/long tap on each 0 day and 'Bump'  as show in the image below



In some countries working with cycles this is often used for unexpected 'snow days' to keep the cycle going afterwards