How to introduce a budgie to the family?

Hi so I just got a budgie a few days ago. He is kind of skittish and he flies (or tries to fly, his wings are clipped) away whenever he's startled. He bites when anyone tries to pet him (birds just don't like to be petted, I guess) and he is very quiet. I've been working on him and he is getting better and hasn't bitten me in a while, but he still tries to fly away. The person that clipped his wings didn't do it well enough, I think because my bird can still fly pretty well. it's just scary because he'll fly really high up and then flop, leaving me to catch him. My family has been dying to hold him, especially my 8 year old sister but I really don't want any of his skittishness to return. So, what is the most less-stressful way a girl can introduce her really sweet but shy bird to the family?