I have searched the internet and I am still baffled by my conures behavior… I find articles about head bobbing with some saying he is irritated and others saying he is trying to interact. However, mine does more than that,… Rio bobes his head up and down fast with his beak open, stops and then moves his tongue around as if eating peanut butter with his mouth open. His is usually chattering too (not squawking). What does it mean?
Before we can try to give you an answer, we need to know the age of your bird. The head bobbing could mean a couple of different things and the birds age will help us to know which meanings this behavior is most likely to be. The more information that you can give the more accurate of an answer we can give you. A video of this behavior would be a big help.
Wolf is correct. Age and circumstances are needed because the same behavior could mean different things: hunger, eagerness to be picked up, annoyance, etc.