How can I send private data to MS Access automatically?

I am trying to create a form that automatically (but securely) sends the submissions to an access database.

How do you recommend sending this data to MS Access while keeping it secure rather than publishing to the web?

To my understanding it seems to me that you wish to send your form submission data to your external ms access database.

If your database supports mysql and php you could export it there as mentioned in this guide here: https://www.jotform.com/help/126-How-to-send-Submissions-to-Your-MySQL-Database-Using-PHP

Alternatively, it is also possible to send data there using a webhook:

 https://www.jotform.com/help/245-How-to-Setup-a-Webhook-with-JotForm 

Another option would be to export your data and manually reimport it into your end: 

https://www.jotform.com/help/374-How-to-export-all-of-your-data-at-once

Lastly, we also have ftp capabilities:

https://www.jotform.com/help/177-How-to-enable-FTP-on-form-submissions 

Which of these options would provide the most security when transferring private information between JotForm and Access?

All of the methods are secure.  Webhooks and using PHP both support SSL and are very secure.  Exporting your data manually to Excel format and importing it manually to your database would give you complete control over the transfer.