You can encrypt the conenction string inside the webconfig, here is an article from Microsoft about this topic : http://msdn.microsoft.com/en-us/library/dx0f3cf2(v=vs.80).aspx
If you sending the connectionstring over a channel its not more secure than the channel. For example sending the connectionstring over HTTP and it will be just plain text, HTTPS and it will be encrypted, over FTP just plan text, and so on...
If you have a webapplication in a shared hosted environment you should be worried about that the provider maybe get hacked.
So just keep the connection string inside the web.config and encrypt it and don't send it around on internet ;-)
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