How to reference an entry field in a guest user form?
So, I found the answer after much digging.

Thanks to this answer https://craftcms.stackexchange.com/a/9831/7962

I see that the entries field type has to be referenced with an additional set of brackets.  My form now works after changing my input to:

&lt;input type="hidden" name="fields[event][]" value="{{ eventId }}"&gt;