I would most definitely use your Master Ball on your legendary bird, Latios or Latias. They can be really hard to run into for a first appearance, so by that point most people are fed up with trying to play games with it. The other legendaries will always be there. If they have a nature you don't like, simply shut off and try again. You can do that with your bird, but you'd have to find it all over again. Of course, if you run into a shiny Pokemon that is know to flee real easily, use your Master Ball. But that's just an exception.