May i suggest looking at this in a different way? We all learn by watching one another, and people can learn from watching us, as well.
1. Don’t worry about making kids feel bad for not wanting to post flyers. This is assuming that what you are asking is a burden, and not worth doing, and that you aren’t worthy of help. Can you be sure that this is true? Maybe the other kids WANT to do helpful things. Maybe helping another person who is suffering will give them a sense of reward. Maybe one of the meanings of life is to learn to help others and have compassion for their pain, and this is a way for them to do that. Maybe seeing that you love your bird so much and miss him will open someone’s eyes to the fact that other living beings besides humans have minds, have feelings, feel joy and pain, and they might begin to care about the welfare of a let bird. That could open the door to caring about all other beings.
Maybe it could take a while for the lesson to sink in. Let’s say the worst happens, and someone makes fun of you for caring about a stupid bird. So what? Maybe they just aren‘t ready for the lesson, but ten years from now they might remember it. It isn’t your problem, what others learn or don’t learn. It’s only your problem to stand up and speak your truth: you had a bird, you love him, he got lost, you are worried about him and would like to have him back. Isn’t there the parable of the good shepherd, who went back out into the night to find a single lost lamb? Aren’t you being a good shepherd to your flock, to look for your lost bird?
2. Why would it be disrespectful to God to use the church friends to help find your bird? Could it also be true that God would be pleased to see church members turn to one another for love and support and help? Isn’t there another parable where god sees every sparrow fall? If god cares about every sparrow, why not every budgie? I don’t think it was about the sparrows, or about small birds…the parable is about every life being valuable and precious. The parable doesn’t say that god will save every sparrow, just that the sparrow is worthy of being seen, and if the sparrow is worthy of being seen, how much more are you worthy? So go to the church group, take a few flyers, tell your story, let people see. Let them know how special these little creatures are, how loving and intelligent. Let them know how much you care about him, and that you aren’t ashamed of loving a small creature, how it teaches you to love all beings and want to help them. I don’t say that you are being called to do this. But it is an opportunity before you, and you can choose what to do. Can you choose to ask for help for Jeff, and for yourself, because this is your lesson to learn - and accept that people will respond according to their own abilities, and that this is their lesson, not yours?
I hope you are able to find Jeff and bring him home. Remember that he will need to be quarantined from the other birds just as if he was any stranger, because he could have picked up a disease in the wild. Never doubt that love is the right path.