You can do a couple of things, actually. Firstly, if you're playing Black/White 2, you can do Funfest missions to collect pass orbs which you can use to purchase a pass power called Exploration Power from using your C-Gear. What it does is allow you to have a higher chance of finding shaking grass, bubbles in the water, and dust clouds while out traveling on routes and caves for a duration of 3 minutes. Another way in which may increase your chances of getting a Drilbur is to go into the Relic Passage and use Super Repels so that you don't encounter other wild Pokemon and run around. Every 256 steps should cause a dust cloud to appear. Without the hinderance of possible wild encounters from the Super Repels, you can walk up to the dust cloud and find Drilbur in there.
Source: Experience
