Take the basic report already in HandsOn Connect called "Total Active Future Occurrences" and we'll perform a few modifications on it to make it very specific and useful.

Click on  a "Save As" and we'll save it as "Occurrences visible on public site".

It already has filters setting the end date & time of the occurrences to greater or equal to today, and occurrence status = active.

Volunteer Opportunity: Status

Volunteer Opportunity: Number of Volunteer Opportunities  (Summarize on this field to get the SUM

Volunteer Opportunity: Invitation Code

Occurrence: Status

Occurrence: Total Connections (summarize as SUM)

Occurrence: Total Confirmed  (summarize as SUM)

Volunteer Opportunity: Status = Active

This way you'll know about opportunities that are not normally visible in search, but ARE in fact active, if you have the invitation code.

To do this, you'll need to remove the grouping on the Volunteer Opportunity Record ID  (you can only group by three items).

And I also recommend moving the Managing Organization field out of the groupings, so that you'll only see Volunteer Opportunity Names in the 'hide detail' mode.

So you're grouping will now be:

Invitation Code:

Volunteer Opportunity Name

Now Click - HIDE Details, Save the report, and Run it.

The total of 'non-invitation code" occurrences is what will appear on your public site search.

You'll also have a summary of how many upcoming connections and 'confirmed volunteers' you have.   (Confirmed volunteers is the number of connections + anon(guests)