I use VS2008 as well for the Silverlight work, VS2008 Professional Sp1. There is a setting that controls where xap goes. You should not need to copy it manually. You may want to try publishing the hosting ASP.NET project which should include the ClientBin folder.
In the ASP.NET host project that is created with the Silverlight project automatically in VS2008, look at the properties by Right Click -> Properties. The last item on the vertical tab should be "Silverlight Applications". You should see your Silverlight project shown is the list. The "Path in Web" should be set to "ClientBin" which is the default location. If you change this default location in object tags in the aspx page, you will have to change the settings here as well.