How old is your child?
I've had plenty of bites from my beardies I've had over time. (Had one aggressive girl that no matter what you did, she would try to bite...She was just demonic to anyone and everyone.) The other bites (besides hers) were from me doing something to the dragon (whether it was intentional or unintentional) that made the dragon spook and get defensive.
If they're adults, they will be able to draw blood, but if they're babies, it feels more like a pinch.
If you want a baby dragon, then yes, you need to continue to pick him up while he's being "aggressive" with you. How else is he going to learn who's boss? If you back down every time he shows a bit of attitude, then he'll learn he's the master and not you.