Gina,
I am fairly sure that the only time a beardy is gonna bite, is if you stick your finger in their mouth while it is open. They do a whole lot of other things, like blowing their beard, turning black and splotchy, and running, and jerking their head. Fallowing Vets orders I have tortured mine, force feeding, giving meds, and general care, the only time mine "bit" me was when I was shoving food down his throat, and did not get my fingers out of the way quick enough. I ended up with one tiny pin prick on my thumb, and it did not really hurt. I talked to the vet, and he said that I would not get sick from it.
The injuries that I got, being new and not knowing how to hold it, consisted of scratches. You have to support their bellies. Three fingers under their tummies of a solid surface like your chest or shoulder. You have to make sure they feel safe, so you do not pick the up and get them situated, you get them situated before their feet leave the ground.