I'm largely in agreement with the others on camera settings.
One distinction is whether you are trying for identification images, proof, or commercial/fine art prints. In the case of the identification and proof, any image is better than no image, so definitely use AF-C Release priority. For Commercial / Fine Art images, Focus priority is better because only perfect images have any use at all.
For perched birds in bushes, I would start with Single Point AF but use manual override if needed. It takes lots of practice to quickly focus and capture your subject. Watch for twigs, leaves, and any small thing in front of your subject that might hinder AF.
I would use the Back Button / AF-On approach for focus. You might only be able to put a sensor on a portion of the bird and need to be able to separate focus from release. Also focus and reframe has disadvantages since the camera will track a subject. If you have nailed focus and try to reframe, it's easy for the camera to think it should track a moving subject. Also keep in mind the center AF sensor is the most accurate.
I use Aperture priority and matrix or center weighted metering with an eye to blinkies and the histogram. I dial in whatever exposure comp is required.
My guess is low light is a problem. AF does not work as well with low light as bright light. Higher ISO reduces contrast and make images look softer. Neil's suggestion of a flash is a good one.
Try some testing on simple subjects - easy birds - to get comfortable with your setup. Then move to more challenging situations like birds in a thicket. You may ultimately require manual focus or manual override a lot more often in a cluttered situation.
Make sure you have enough DOF. A D300 with a 300 f/2.8 and teleconverter (aperture of f/4) has a DOF of half an inch at 15 feet - less if you are closer. At f/8 you double that to an inch. You better be right on the money if you expect your images to be sharp. Shutter speed can be a problem at f/8 in the shade, so again you may need a flash.