Hi Christina,
Have you ever tried shooting in spot metering and spot focus mode?
On the back of your camera there is a button that says AE-L and AF-L. This button can either lock AF or AE. Set up the camera so the button locks Exposure. When shooting very bright subjects in direct sunlight you focus on the bright area and push the AE-L button with your thumb, now you can recompose and half-press the shutter button to focus. The exposure will be locked on the bright area as long as you keep the AE-L button pressed.
I had a serious problem trying to shoot a white flower in an area with a dark green background, with matrix metering turned on. The flower would be overexposed and the background correctly exposed. Spot metering turned on and the problem was solved. You may burn out your background but will get the exposure on your subject right.
Maybe it does not work so well on birds, next time I shoot a white bird in bright sunlight I will try it. It is not always easy to lock exposure, pressing the AE-L button and holding it in while re-composing, you need to practice a bit.
You practice this method of exposure on any subject and see the outcome.
Doing this will teach you a lot about the Zone System of exposure.
Maybe you will find this very interesting:
http://photo.tutsplus.com/articles/t...s-zone-system/