Hello, Suzan. Thanks for passing by. Regarding your question:
A) Capture: Use central photometry (not matrix) and put the bird in the center (for light metering). That should properly expose the bird. Remember to leave some room for "crop composition", as you centered the bird.
B) Post Processing: Work with lights and shadows curves. Normally, in such situations, you will raise shadow levels and pull down the lights a little.
Then you can do your usual PP, in the way you prefer to do it (sharpen, noise reduction, saturation and contrast levels, etc), ok?
Kindest regards,