Like Dave said in so many words you cannot bond with your bird by giving it handfeeding formula, that is for very young babies.
You bond with your bird by treating it with kindness, providing for its needs, spending time with it and behaving consistently so that it learns to trust you and then the bonding comes right after. This happens very quickly in a very young bird but an older bird will take longer, sometimes much longer since it has had relationships with other people before coming to you.
So that "SPECIAL" bond you missed, forgetabouutit, you haven't missed anything, you have to make it happen all by yourself.