Take the tube out (mark the valve placement on the tire beforehand), inflate it, submerge in water. You don't even need to submerge all of it at once, if you don't have a tub large enough - you can go around the whole tube submerging it bit by bit. A leak like the one you described would show as small air bubbles forming and escaping one by one (larger leaks would cause a continous flow of bubbles), so take your time and pay attention. There will probably be some tiny bubbles sticking to the tube where some dust particles are, so brush them away and observe if new ones aren't forming in the same place. After you find the leak, the location of the culprit shouldn't be too hard anymore.
In my experience, the submerging has always worked; if there is a leak, it shows.