It is possible to password protect the submissions for one of my forms?

Sadly, there's no way to password protect submissions. Also, it's worth noting that only you as the account owner will have access to your Submissions Page. No one will be able to see your Submissions Page not unless you share your JotForm credentials with them.

I also took the initiative of checking your account and confirmed you don't have any Subusers added. This means that no one else can view your Submissions Page except you.

In case you're referring to something else or we misunderstood your question, then give us more info so we can better assist you.

That answers my question.  If I were to setup a subuser account, would that give the subuser their own account and access to their forms only?

If you set up a sub-user account then you may decide what this sub-user can do with your forms, you decide which forms to share with it, if the sub-user is allowed to edit the form or if the sub-user is allowed to view the submissions.

Sub-users can still create forms, but all the forms will be created under your account or the main account, if you want to allow them to create forms in their own account they will need to have one or more forms created prior to be added as sub-users.

Here're more  details about how to share forms with a sub-user account and more info about it: How-to-share-forms-with-a-sub-account-user

On the "My forms" page, you can check the box beside a form and then select the "Reports" option.

From that menu, select "Add a report".

A menu will open asking what format you prefer for your Submissions report (Excel, HTML, CSV, etc).  Select your preference. Click next.

A menu will open that provides fields you'd like to include/exclude in your report. At the bottom, be sure to select the "Password Protect" option.  When you do this, it will ask you for a password.

Once complete, it will say "Report created successfully" and provide a link to your report, which will require your password to access. 

Done!