I've lost count of the number of times I've been ACCIDENTLY bitten by a skink or a dragon , always been my fault while I was hand feeding and not paying 100% attention the task.
Very likely the bite was out of fear. Stranger pickup dragon and tries to force to have a
bath. If I was the dragon I'd take a piece too.
If the dragon is a hatchling , as already suggested , leave a very shallow acrylic rock look water dish in the tank with water only a 3mm - 5mm dead (no depth than the side spike fringes on the dragon's body. when in shed many hatchlings will use the water to help alleviate the itchiness and help loosen the old skin.
Regarding
bathing in general : not necessary for a bearded dragon
>> will only
hydrate a dragon if they actually drink while in the
bath
only
bath when necessary (unless you have a dragon who loves to play in the
bath , otherwise
bathing is not worth the stress on the dragon or the risk of asperation of the water into the lungs or even drowning)
ie
<<< impacted
<<< very soiled
<<< to help remove a stubburn area of shed
<<< betadiene baths for sores and open injuries