Open up the idle air bleeds a few thousands of an inch at a time until the drip stops. This is best done with a complete set of number drills (60-100) and a pin vise. If you do not have these tools/drills then don't attempt this procedure, you can easily destroy the carb if you do this improperly. With Holley carbs you can usually solve this problem with a venturi booster change.
I have also seen a modification where a tiny hole was drilled in the tip of the brass tube, this effectively reduces the pulsation of vacuum that is drawing the fuel out and make the idle circuit less sensitive to these fluctuations. Mind you this was done to a very radical alky sprint car engine, I would not recommend this mod for your mildly tuned engine.
Are you positive the air bleed circuit is perfectly clean? This circuit can be impossible to clean on a used carb and usually means a scrap carb if it is filled with the yellow/white fuzzy's. Air flowing throught the holes does not guarantee it is clean. Double check everything before drilling anything, I doubt you need to drill the bleeds with such a mildly tuned engine. Use a long horse hair or fishing line to probe the circuit (DO NOT USE metal wire!!). I have used ultrasound cleaning to good effect to salvage scrap carbs before but with only a 50% success rate when the bleeds are compromised. I know some people have pulled the bleeds and cleaned them and then pressed in new bleeds but make sure you can get new ones before doing this, they can be fabricated, but not easily (ever drill a 0.007" hole?).
Outlawed tunes from outlawed pipes