First, most web site databases are behind firewalls and you may have to have the hosting company allow SQL Server traffic from your IP address to pass through the firewall. Talk to your hosting support company to discuss this with them.

Second I would suggest first try to connect to the database with SQL Server Management Server. It gives you the most control on the connection.

Once you have connected you could try using the Import/Export wizard in SSMS to try to import the data. If that works you can create a job from it to either run automatically or manually.