We use webapp web.xml for configuration parameters. I think that's the recommended way to do it. That also makes it local to your webapp, which would be local to your servlet environment.
I don't know how your system returns the Tomcat /bin directory -- on our installation of Tomcat 5.5.23, user.dir returns the top of the Tomcat directory. /bin would be a subdirectory under it.
context.xml for a host certainly works for us -- if your catalina output says it is being ignored, it's probably because of a problem in it or an overriding specification somewhere else.