I personally use the eyedroppers. It's best to find ones made of plastic. When they get a little bigger their bite is sufficiently strong to break the glass ones.
The advantage of the eyedropper is that you can control the amount coming out much better than with a syringe.
Also aim is better.
I agree with
@AHBD about how often to offer water. Babies are generally under higher heat and are smaller (obvious I know, but it leans into my reasoning) both of those factors leads to them dehydrating quicker than larger beardies.
Even with an eyedropper (or your finger) go slow, what's a tiny drop to us is huge to them. They could become aspirated fairly easily.
As for bowls of water, they generally will just poop in them and cause unsanitary conditions pretty quickly.
Most beardies won't drink from standing water. And if they will and they poop in it and then drink it the risk if a Cocidia outbreak becomes an almost certainty. (Cocidia has to be pooped out and reingested to multiple) It's also a real pain in the butt to get rid of once you have an outbreak.