Say I have an ASMX web service, MyService. The service has a method, MyMethod. I could execute MyMethod on the server side as follows:
MyService service = new
I looked back at this question and I think what you're facing is that the ASMX code will be built into a DLL with a random name as part of the dynamic compilation of your site. Your code to look up the type will, by default, only search its own assembly (another App_Code DLL, by the looks of the error you received) and core libraries. You could provide a specific assembly reference "TypeName, AssemblyName" to GetType() but that's not possible in the case of the automatically generated assemblies, which have new names after each recompile.
Solution.... I haven't done this myself before but I believe that you should be able to use something like this:
System.Web.Compilation.BuildManager.GetType("MyService", true)
as the BuildManager is aware of the DLLs it has created and knows where to look.
I guess this really doesn't have to do with Web Services but if it were your own code, Daren's right about Facade patterns.