The idea is to find a balance between gliding/freefall and flapping or diving to place your character on a good trajectory. Hopefully you won't get a high score by just letting the bird bounce off the bottom of the screen, because there shouldn't be much to catch. So basically you have to periodically fly to the top of the screen and aim for a good trajectory, or occasionally dive for a berry. For reference, I can get scores in the 9 thousands using this strategy (in a 3 minutes game).
Always glad to receive feedback :)