Cyberduck is a free WebDAV client by Swiss Made Software that will allow you to connect to your BigCommerce remote folders.
How to enable WebDAV
1.) Enable WebDAV - From your BigCommerce Control Panel click "Users" in the top right.
2.) Click edit on the User that is going to have WebDAV enabled.
3.) Scroll down to the bottom of the page and place a check on Enable WebDAV and copy the Path.
4.) Click Save.
Connecting to WebDAV with CyberDuck
1.) Open CyberDuck and click Open Connection.
2.) Select WebDAV (HTTP/SSL) from the dropdown.
3.) Paste the WebDAV path you copied from the above steps into Server.
4.) If anonymous login is checked, uncheck it. Enter the username and password for the User Account you enabled WebDAV.
5.) Click More Options and in the Path field type /dav.
Click connect. You should now be connected to your BigCommerce folders, and can manage them just like a normal FTP program.