Common authentication schemes are well-defined and, while not perfect, are known entities. The worst thing you can do is "roll your own" in security.
I assume by your comment "pass username and password to the method", you mean you would like to have access to the credentials used to access your web service. This is fine, but don't pass credentials as parameters to your method.
Based on your description, basic authentication over SSL should provide you sufficient protection for your application. This would work in a non-trusted environment (i.e. across unknown networks) and should be easy enough to implement on the client-side.