There's a very real tendency when we use a long lens to fill the frame as much as we can, which is what you've done here. It's great that you can get that close to wild birds, they tend to be very wary, but you'd have done better to have used less focal length and got the whole bird in shot including some of the background. Magazines often prefer shots showing the bird and some it's surrounding habitat. Have a look at Dod's bird shots to see what I mean. See the difference pictorially too if you wanted to frame any of these shots? Try to think of the overall shot and how it succeeds as a picture rather than just being a close-up of a birds head. You can get away with this with larger more dramatic birds, raptors etc., but smaller birds often benefit from less focal length and leaving yourself room to crop is usually desirable.
Think about getting a bird feeder or bird table and siting it somewhere advantageous for your shots where you can get a nice oof background.
You often need the patience of Job for these sort of shots, but it's very rewarding when you pull them off.