I can tell you what I did in my experience about this.
That screw at the bottom of the carb leaks. It's leaked on most of the builds I do. Common sense tells me that the purpose of that screw is ONLY for draining the fuel before removing it and tinkering - it could serve no other purpose. I too tore down and rebuilt my carb many times in hopes of finding a leak around the gas intake nipple or gasket, but alas, no dice. So, I just leave it alone and let it drip!
The solution I found for this is... turning off the petcock from the tank! It's a pressure driven fuel line powered by gravity, this is why there's no fuel pump, this is why the tank is above the motor. When you stop the pressure from pushing gas unrestricted (due to the gas tanks venting), it will leak for a minute, but all that will leak is the gas that has collected under the float, and even then - not all the gas from that chamber will leak out! So, if you're turning off your petcock and you see leaking, that's why - don't freak out.
Personally, I don't mind the leaking. It's leaking unburnt fuel out of the exhaust and out the carb drain screw. Eh. I leave the petcock on all the time (with the exception of storage for weather reasons). The reason I leave it that way is so that when I fire it up the next morning it fires up immediately without setting the choke. I know it's slightly irresponsible maintenance, but there's a reason behind it at least.
NOTE!!! If you see a leak like this, it is a VERY MINOR leak. If you are noticing a very MAJOR LEAK, then check your gas tank and fuel lines. My first build I didn't think twice about mounting the gas tank above the metal brackets for the brake line (the ones welded to the frame). After a season of riding I lost a full tank in about an hour while it was parked, and there were two holes! One was about 2mm, the other about 1mm. The vibrations of the motor caused the brake line brackets to bore holes. I was able to remedy this by JB Welding the holes shut, and placing 5 or so strips of denim between the tank and the frame. I considered using a cut tire, which would work better, but denim was more easily accessible. So, before you diagnose it as the carb drain screw, be sure you have checked everywhere else!