You cannot connect to a network drive by authenticating in this manner. Furthermore, there isn't a .NET class that accomodates this.
You have two options, invoke the Win32 API using interop, or spawn a "net use" command via the command interpreter.
This article[
^] shows how to map a drive using interop. You don't need the complexity of this whole project, but scanning the source code will show you the essential steps.
Note, that you don't actually have to map a drive letter to do this, you can just use this method to connect to the remote share without mapping it. Once you have done so, you can invoke File.Copy() without trying to embed the credentials.