There are two ways to open FBA Site from SD :
1. Authenticate from IE First : Open your FBA site from IE, Login as Administrator and choose to "Login Automatically" , then open the site from SharePoint Designer. The SharePoint Designer will uses the authentication cookie to open your FBA site.
2. Extend your FBA site from the central administrator. this will create another IIS website with a windows authentication by default. open the site using SD by providing the windows auth. URL of your site.