You can't get it before chargestone cave I'm afraid, but you can get drilbur in dust clouds when you are in chargestone cave. As for making them appear there is no technique, just a small chance to make onr with every step. As for when you see a swirling dust cloud in chargestone cave I suggest to use a repel whilst approaching it, because if a wild pokemon attacks you whilst going towards it when you exit the battle the dust cloud will be gone. The same goes for shaking or bubbling spots.
Hopes this helps - James