I have successfully trained all my beardies to drink from the water bowl in their tanks using a trick I learned having chameleons.
The key? Moving water.
A friend told me that chameleons will only drink moving water. That makes sense. In the wild, stagnant water is more likely to be bacteria or predator filled. Most bearded dragons will drink in the bath because the water around them moves as they move.
When I get a new Beardie, I fill up their water dish, set them near it, and then flick my fingers in the water to make it move. The movement catches their eyes and, almost always, they will lick their lips. For some of my stubborn beardies, I will drip water on their lips to help them. 95% of the time, they will start to drink on their own from the bowl.
It took me almost two years to train Ziggy to drink water from his dish. He was my most stubborn guy. He wouldn't ever drink-- not even in the bath. I finally trained him to drink from a syringe and then transitioned him to his water bowl. Now he drinks on his own whenever I refill his dish.
A drinking Beardie will flatten himself like a pancake, close his eyes, and slowly drink. In a bath, they will puff up and then flatten. It's all instinct for them. They can drink for a minute to 7 minutes. After they are done, you will often see them breathing heavily with their mouths open. They may even spit up extra water. This is all totally normal. Try not to handle a Beardie that has just drank a lot because they will easily spit out the water.
I make sure to fill up all my beardies' water bowls once a week with them watching me. That is almost always enough to trigger a drinking reflex.
Oh, and after drinking water, the next few poops will be very wet and squishy. Totally normal.
Any other questions?