So where exactly is the Access database (mdb file) located? You say it's on the users computer, but then make it sound like it is being used by your web server.
Is the users computer also being used as a web server? (this is probably bad)
Is the database on a shared folder on the users computer, being access by the webserver (this is definitely bad due to less then perfect file locking, unless the web server is doing read only operations)
If the web server is a seperate machine and your environment is Active Directory, or if the server and users machine are the same, you can just set permissions of the database mdb file to only allow the user and the account the web server runs under to access it.
Alternatively, if the file is on a share, you could set the permissions of the share folder to only allow those 2 accounts.