For the longest time, my budgie would walk away from my finger if I tried to ruffle the feathers around his head, face and neck. After having him for about two months, he was in the car with me for a long drive stuck in traffic in his carrier. I had my fingers on the bars of the carrier and he began to beak them playfully and make cute little chirps. I opened the carrier and he let me approach his beak and face with one finger and I was able to pet him there. Now I can usually approach him and he'll accept petting.
Is your bird or are your birds very cuddly with you? Do they like when you pet them?