How to password protect a field in access?
The following is solely based on Internet research so your mileage may vary.

It appears that you can password protect certain tables.  This article walks you through the process.  Essentially what you need to do is create a workgroup.  Once your workgroup is created you login into your database via a link that workgroup creation wizard produces, and you can set the permissions for all of your users.

I also found this answer on StackOverflow that says it can't be done so who knows.

The more robust solution would be what is suggested as an alternative in the StackOverflow answer above.  Just upgrade to SQL Server Express.  That should be a low cost solution that will offer a nicer, more manageable RDBMS in my opinion.  However I recognize that transition isn't always an option.