How do I share the form with another person without making it public?

how do I share the form with another jotform user in my company without making it public

As forms can be viewed by anyone with a link to them, one solution I would suggest, in order to restrict access to the form between you and the other JotForm user, is to set up a form condition that hides all the form fields until the correct word is entered in a field you may name "Show Form" or so.

This way, while anyone could open the form, they would see only one field, and when you enter the correct word the actual form fields show up.

We have a guide on how to show or hide fields based on user's answer here: https://www.jotform.com/help/316-How-to-Show-or-Hide-Fields-Base-on-User-s-Answer

I hope this helps. If you need further assistance please let us know. Thank you.